Answer:
The angle the projectile was fired is [tex]45^o[/tex]
Explanation:
Recall the formulas for maximum height and ranges for a projectile fired with initial velocity "v" at an angle [tex]\theta[/tex]:
[tex]h = \frac{v^2\,sin^2(\theta)}{2\,g}\\R=\frac{v^2\,sin(2\,\theta)}{g}[/tex]
we can use them to solve for the angle by first isolating the value [tex]v^2[/tex] which is common in both equations:
[tex]v^2=2\,h\,g/sin^2(\theta)=2\,(15)\,g/sin^2(\theta)=30\,(g)/sin^2(\theta) \\ \\v^2=R\,g/sin(2\,\theta)=60\,(g)/sin(2\,\theta)[/tex]
and now, making those to expressions equal and using the formula for the sine of a double angle, we get:
[tex]\frac{30\,(9.8)}{sin^2(\theta)} =\frac{60\,(g)}{sin(2\,\theta)} \\30\,(g)\,sin(2\,\theta)=60\,(g)\,sin^2(\theta)\\sin(2\,\theta)=2\,sin^2(\theta)\\2\,sin(\theta)\,cos(\theta)=2\,sin(\theta)\,sin(\theta)\\cos(\theta)=sin(\theta)[/tex]
This happens when [tex]\theta=45^o[/tex]
Find the acceleration of a body moving with uniform velocity
Answer:
The derivative of a constant term is always 0. So the acceleration of the body would be zero. Hence, the acceleration of a body moving with uniform velocity will always be zero.
A wire of length 5mm and Diameter 2m extends by 0.25 when a force of 50N was use. calculate the
a. Stress of the wire.
b. Strain of the wire
Answer and Explanation:
Data provided in the question
Force = 50N
Length = 5mm
diameter = 2.0m = [tex]2\times 10^{-3}[/tex]
Extended by = 0.25mm = [tex]0.25\times 10^{-3}[/tex]
Based on the above information, the calculation is as follows
a. The Stress of the wire is
[tex]= \frac{force\ applied}{area\ of \ circle}[/tex]
here area of circle = perpendicular to the are i.e cross-sectional i.e
= [tex]\frac{\pi d^{2}}{4}[/tex]
= [tex]\frac{\pi(2\times 10^{-3})^2}{4}[/tex]
Now place these above values to the above formula
[tex]= \frac{4\times 50}{\pi\times 4 \times 10^{-6}} \\\\ = \frac{50}{\pi}[/tex]
= 15.92 MPa
As 1Pa = 1 by N m^2
So,
MPa = 10^6 N m^2
b. Now the strain of the wire is
[tex]= \frac{Change\ in\ length}{initial\ length} \\\\ = \frac{0.25\times 10^{-3}}{5}[/tex]
= [tex]5 \times 10^{-5}[/tex]
Imagine that you are using a similar computer simulation to conduct an experiment on ph value of different liquid hand soap solutions and water. What is a potential source for error in such a computer model?
Please help!!
The computer model would rely on the labeled pH values of various hand soap brands however the labled pH value might not be entirely accurate, which could comprise the accuracy of the computer model.
Inaccuracies in the simulation's underlying chemistry model could be a potential source of mistake in an experiment involving the pH values of several liquid hand soap solutions and water.
The outcomes could differ from actual behavior if the model does not adequately represent the intricate chemical interactions that control pH fluctuations. Furthermore, because they might not exactly match the varied properties of real hand soap solutions, the simulation's assumptions and parameters could introduce bias. Disparities between simulation results and empirical findings may also result from inadequate consideration of temperature impacts and ambient factors. To reduce such possible mistakes, careful simulation validation against empirical data and chemistry model modification are required.
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lab safety test Safety goggles and an apron must be worn when handling chemicals labeled corrosive because they:________.
Answer: React with the skin
Explanation:
lab safety test Safety goggles and an apron must be worn when handling chemicals labeled corrosive because they React with the skin
Two 110 kg bumper cars are moving toward each other in opposite directions. Car A is moving at 8 m/s and Car Z at −10 m/s when they collide head–on. If the resulting velocity of Car A after the collision is −10 m/s, what is the velocity of Car Z after the collision? 10 m/s −8 m/s 8 m/s 10 m/s-
Answer:
it will be 8ms-1
Explanation:
MaUa+MbUb=MaVa+MbVb
An athlete runs four laps of a 400 m track. What is the athlete's total displacement?
Answer:
○ 0 [tex]\checkmark[/tex]
Explanation:
Even if the athelete runs four laps of a 400 m track, its displacement will be 0 because the displacement is the shortest distance from its to final position. And, here the final and initial position is same since he comes to its initial position after covering certain distance. So, displacement is 0.
A pulley system is made of 3 pulley write its velocity ratio
Almost 3 times fast than normal pulley system
mark me
An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley, the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The child’s true weight is 320 N, and the chair weighs 160 N. (a) Show that the acceleration of the system is upward and find its magnitude. (b) Find the force the child exerts on the chair.
Answer:
(a) 0.42 m/s²
(b) 83 N
Explanation:
Assuming g = 10 m/s².
Draw free body diagrams for the child and the chair.
There are three forces on the child:
Tension force T pulling up,
Weight force Mg pulling down,
and normal force N pushing up.
There are three forces on the chair:
Tension force T pulling up,
Weight force mg pulling down,
and normal force N pushing down.
Sum of forces on the child in the y direction:
∑F = ma
T + N − Mg = Ma
Sum of forces on the chair in the y direction:
∑F = ma
T − N − mg = ma
Add the equations together to find the acceleration.
2T − Mg − mg = Ma + ma
a = (2T − Mg − mg) / (M + m)
a = g (2T − Mg − mg) / (Mg + mg)
a = (10 m/s²) (2 × 250 N − 320 N − 160 N) / (320 N + 160 N)
a = 0.42 m/s²
Plug into either equation to find the normal force.
T + N − Mg = Ma
250 N + N − 320 N = (320 N / 10 m/s²) (0.42 m/s²)
N = 83 N
64. A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance
Answer:
=33 .3×10^6Ω
=33.3M Ω
Explanation:
We were told to calculate the Resistance value,
Given the heart pacemaker fires as 72 times a minute, which is the time constant
Then we can convert the pacemaker fires of 72 times a minute to seconds for unit consistency.
1 minutes= 60secs
Then ,Time constant τ=60secs/72=0.8333 seconds
Time constant τ can be calculated using the formula below
τ= RC
Where R= resistance
C = capacitance
Then making RESISTANCE subject of formula we have
R=τ/C
But Capacitance=25.0-nF = 25×10^25F
Substitute the values we have
R=0.833/25×10^25
=33 .3×10^6 Ω
But can still be converted to M Ω= 33.3M Ω
Therefore, the resistance is 33 .3×10^6 Ω or 33.3M Ω
NOTE: 1M= 10^6
The value of the resistance will be "3.33×10⁷ Ω".
Resistance based problem:According to the question,
Capacitor, C = 25.0 nF
60 sec - 72 fires
now,
Time for 1 fire,
[tex]t = \frac{60}{72}[/tex]
[tex]= \frac{5}{6} \ sec[/tex]
Now,
⇒ [tex]V = V_0 (1-e^{-\frac{t}{RC} })[/tex]
[tex]0.632 V_0=V_0(1-e^{\frac{-\frac{5}{6} }{R.25 n C} })[/tex]
[tex]e^{-\frac{1}{R\times 30\times 10^{-9}} } = 1-0.632 = 0.368[/tex]
[tex]= 2.72[/tex]
By taking "log" both sides,
⇒ [tex]ln \ e^{\frac{1}{R\times 30\times 10^{-9}} } = ln \ 2.72[/tex]
hence,
The Resistance be:
⇒ [tex]R = \frac{10^9}{30}[/tex]
[tex]= 3.33\times 10^7 \ \Omega[/tex]
Thus the above approach is right.
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If 60 L of a gas are at 4 atm and 27 C °, what pressure would it have if the volume is 40 L 127 C °?
Answer:
8 atm
Explanation:
Ideal gas law:
PV = nRT
where P is pressure, V is volume, n is moles, R is universal gas constant, and T is absolute temperature.
If n is constant:
PV / T = PV / T
(4 atm) (60 L) / (27 + 273) K = P (40 L) / (127 + 273) K
0.8 atm = 0.1 P
P = 8 atm
explain the delay in hearing of a sound
Answer:
Humans naturally have what's known as binaural hearing, which is the ability to hear in two ears.
A car accelerates at a rate of 3 m/s^2. If its original speed is 8 m/s, how many seconds will it take the car to reach a final speed of 25 m/s?
Answer:
[tex]\Large \boxed{\mathrm{5.67 \ seconds }}[/tex]
Explanation:
[tex]\displaystyle \mathrm{acceleration \ = \ \frac{final \ velocity - initial \ velocity }{elapsed \ time}}[/tex]
[tex]\displaystyle A \ = \ \frac{V_f - V_i }{t}[/tex]
[tex]\displaystyle 3 \ = \ \frac{25 - 8 }{t}[/tex]
[tex]\displaystyle 3 \ = \ \frac{17 }{t}[/tex]
[tex]\displaystyle t \ = \ \frac{17 }{3} \approx 5.67[/tex]
ball is thrown upward from a window that is 12 m above the ground. The ball reaches a maximum height of 4 m above the window before falling all the way down to the ground. What distance did the ball travel?
Answer:
20 m
Explanation:
The ball travels 4 m up, then 16 m down. It travels a total distance of 20 m.
a body weighs 100newtons when submerged in water. calculate the upthrust action on the body
Answer:
Upthrust = 20 N
Explanation:
The question says that "A body weighs 100N in air and 80N when submerged in water. Calculate the upthrust acting on the body ?"
Upthrust is defined as the force when a body is submerged in liquid, then liquid applies a force on it.
ATQ,
Weight of body in air is 100 N
Weight of body in water is 80 N
Upthrust is equal to the weight of body in air minus weight of body in water.
Upthrust = 100 N - 80 N
Upthrust = 20 N
So, 20 N of upthrust is acting on the body.
1
A force 2ON acts at a distance of 2n from a pivot.
what is the moment
force about the pivot
Answer:
[tex]\large \boxed{\mathrm{40 \ Nm}}[/tex]
Explanation:
[tex]\sf Moment \ (Nm) = Force \ (N) \times Distance \ from \ pivot \ (m)[/tex]
[tex]M=20 \times 2[/tex]
[tex]M=40[/tex]
2 Which invention was crucial to the development of cell theory?
Answer:
I guess i would say the microscope
Explanation:
Because of the microscope, we can see the cells.
Exercise b) 1) Fill in the blanks with the appropriate word: a) The pressure exerted by the air in atmosphere is called b) Pressure is the applied per unit area, c) The pressure ........as the depth of liquid increases. d) The SI unit of density is Az object fisats on water if the ...of the object is leva
Answer:
atmospheric pressure
b)
c)increases
d) ....
A skydiver falls toward the ground at a constant velocity. Which statement best applies Newton’s laws of motion to explain the skydiver’s motion? An upward force balances the downward force of gravity on the skydiver. The skydiver’s inertia is zero, which no longer allows for acceleration. An unbalanced force pulls the skydiver toward the ground. The mass of the skydiver is so great that there is no acceleration.
Answer:
The answer is (a.) An upward force balances the downward force gravity on the skydiver
The skydiver is falling at a constant velocity because the upward force is balancing the downward force of gravity. According to Newton, the opposite force balance each other. This is stated in Newton's second law of motion.
The statement that best applies Newton’s laws of motion to explain the skydiver’s motion is that An upward force balances the downward force of gravity on the skydiver.
Newton's 3rd law often applies to skydiving.
When gravity is not acting upon the skydivers they would continue moving in the direction the vehicle they jumped from was moving.
If no air resistance takes place, then the skydivers would still accelerating at 9.8 m/s until they hit the ground.
The skydiver after leaving the aircraft will accelerates downwards due to the force of gravity
usually as there is no air resistance acting in the upwards direction, and there is a resultant force acting downwards, the skydiver will accelerates towards the ground.
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A position of a particle moving on an x axis is given by x=7•4 + 9•2t - 2•1 t^3, with x in meters and t in seconds. what is its velocity at t=3•5s? is the velocity,or is it Continuously changing?
Answer:
The velocity at that time would be [tex](-67.975\; \rm s)[/tex]. The velocity of this particle is continuously changing.
Explanation:
Differentiate the expression for position [tex]x[/tex] with respect to time [tex]t[/tex] to find an expression for velocity.
[tex]\begin{aligned}v(t) &= \frac{d}{dt}[x(t)] \\ &= \frac{d}{dt} \left[ 7.4 + 9.2\, t - 2.1\, t^{3}\right]\\ &= 9.2 - 6.3\, t^{2}\end{aligned}[/tex].
Hence, at [tex]t = 3.5\; \rm s[/tex], velocity would be [tex]v(3.5) = 9.2 - 6.3 \times (3.5)^{2} = -67.975\; \rm m[/tex].
Since velocity [tex]v(t)[/tex] changes with time [tex]t[/tex], the velocity of this particle is continuously changing.
calculate the average speed of an athele who runs a distance of 100m in 16 s and an additional of 400m in a 44s
Explanation:
speeds = distance/time
=100/16
=6.25m/s
second speed is;
400/44 =9.09
av. speed = total speed /n
= (6.25+9.09)/2
=7.67 m/s
Question 5
Calculate the kinetic energy of a car (m - 800 kg) moving at 15 m/s. Write your answer to the nearest whole number in the blank space
provided. Only write the numerical value of the answer without units. Do not leave any space in between numbers.
Answer: Joules
Answer:
90,000Explanation:
[tex]m =800kg\\v = 15\\\\K.E = \frac{1}{2}mv^2\\ K.E= \frac{1}{2} \times 800\times 15^2\\= 400 \times 225\\= 90000 joules\\= 90 kilojoules[/tex]
Need help finding the average speed.
Explanation:
To find the average of these numbers, we just have to add the three numbers together and divide by 3.
2.07 + 0. 74 + 1.33 = 4.14. 4.14 / 3 = 1.381.09 + 1.40 + 0.31 = 2.8. 2.8 / 3 ≈ 9.3333333/ 9 1/30.95 + 1.61 + 0.56 = 3.12 / 3 = 1.040.81 + 1.89 + 1.08 = 3.78 / 3 = 1.26what is space in detail?
Answer:
Space in the astronomy and cosmology space is 3 dimensional region and earth atmosphere end is called space.
Explanation:
Space is the everything of the top earth atmosphere moon, starts, milky way, black hole and GPS satellites an distant,space also called between stars,moon,planet.
Space is all the extends far in all directions, space is finite unbound space surface of the earth has finite are no beginning or not end.
Space contains there are three dimensions is called 3 D space,an space is to refer an interval during signal transmitted also used by the character, bytes, words and octets in digital signal.
space is that term can refer to various in science, communications and mathematics,and maintain orbits for responsible time, space is usually to begin at the lowest attitude satellites can maintain orbits.
space coordinates are uniquely define the location of any particular point and that continuum requires more than coordinates,and the number of dimensions and conventional space or digital communications during the signal represents logic is 0 words in a digital signal.
liquids with convex meniscus
Mercury in a glass tube.
How much heat does 25 g of aluminum lose when cooled from 100 ° C to 20 ° C? Express your result in BTU
Answer:
1.7 BTU
Explanation:
q = mCΔT
q = (25 g) (0.9 J/g/°C) (100°C − 20°C)
q = 1800 J
q = 1800 J × (1 BTU / 1055 J)
q = 1.7 BTU
A control clinic offers a program that guarantees a weight loss of up to 0.46 kg in one week. Express the weight loss in a ratio of milligrams per second.
Answer:
0.76 mg/s
Explanation:
0.46 kg/week × (1 week / 7 days) × (1 day / 24 hrs) × (1 hr / 3600 s) × (1000 g/kg) × (1000 mg/g) = 0.76 mg/s
Bagaimanakah pelembapan bagi suatu sistem ayunan dapat diatasi dengan resonans?
Answer:
Those reaction in which one element replaces another element form its place is called Single displacement reaction
What did Bohr's model of the atom include that Rutherford's model did not have?
a nucleus
energy levels
electron clouds
smaller particles
Answer:
The correct option is energy levels
Explanation:
Rutherford's model of an atom suggests that an atom has a tiny positively charged central mass (now called the nucleus) which is surrounded by electrons (negatively charged) in a cloud-like manner.
Bohr's model went a bit further than the Rutherford's model in describing an atom by suggesting that the electrons which surrounds in the nucleus travel in fixed circular orbits. This description by Bohr was able to describe the energy levels of orbitals which assumes that smallest orbitals have the lowest energy while the largest orbitals have the highest energy.
Answer:
energy levels
hope this helped!
Explanation:
Which is
easier
Push
or pull.
when force is at angle
Answer:
pull
Explanation:
because when you push there is one component of force that adds to tge weight of body and hence there is more friction. Whwn you pull the vertical component of force is against the weight of body and hence friction is low.
Once a scientist has made a hypothesis, what would they typically do next? (2 points)
a
Analysis
b
Testing
C
Research
d
Sharing
Answer:Testing
Explanation:Once a scientist has made a hypothesis, what would they typically do TESTING nextn
Once a scientist has made a hypothesis, they would typically do testing, therefore the correct answer is option B
What is the scientific claim?Scientific claims are statements made in science based on an experiment.
These Scientific claims are backed by the experimental data and their true results obtained from scientific investigation and experimentation.
When a scientist performs a fair test is one in which all other circumstances are maintained while just one variable is changed at a time.
Scientists frequently discover that their hypotheses and predictions were not supported by the results of their experiments. In these situations, they will communicate the findings of their experiment before revising their original hypotheses and predictions in light of the new knowledge they have gained.
The right response is option B because once a scientist has made a theory, they usually do testing.
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