Need help with these prelab questions. UPDATE: THERE IS NO ANGLE FOR THE RAMP, J

Question

Need help with these prelab questions.

UPDATE: THERE IS NO ANGLE FOR THE RAMP, JUST USE VARIABLES IN THE FINAL ANSWER.

Please use clear handwriting or typed answers. Thank you!

Lab 5: 2-D Kinematics and Projectile Motion

Pre-Lab Questions

In one of your experiments, you will roll a marble down a ramp to provide an initial horizontal velocity. Suppose you start the marble at rest (vo = 0 m/s) and it travels a distance of, d, down the ramp. Use 1-D kinematics to predict the velocity of the ball (vf ) at the bottom of the ramp. Hint: the acceleration of the ball down the ramp is 9.81*sin() m/s2 where is the angle of the ramp. Record you answer in variables (you will calculate the velocity with magnitudes when you perform the experiment).

Use the kinematic equations to derive a general equation for the time it takes a ball dropped from rest at vertical height, h, to reach the ground.

Use the result from Question 2 to write a general equation for the distance travelled by a projectile that is rolling off a table of height, h, with a horizontal speed, v0x.

Explanation / Answer

The height of the ramp using trigonometry will be:

H = d sin(theta)

we know from conservation of energy

PE = KE

m g d sin(theta) = 1/2 m vf^2

vf = sqrt (2 g d sin(theta))

------------------------------------

We know that

S = ut + 1/2 at^2

H = 0 + 1/2 g t^2

t = sqrt (2H/g)

------------------------------------

we know that

D = v t = v0x t

D = v0x sqrt (2H/g)

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