- 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(θ) m/s2 where θ is the angle of the ramp.

Record you answer in variables.

(you will calculate the velocity with magnitudes when you perform the experiment).

2.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.

3.Using the result from Question 2 what would be a general equation for the distance travelled by a projectile that is rolling of a table of height, h, with a horizontal speed, *v0x*

4.The range of projectiles is dependent on the velocity and angle of the launch. Using the kinematic equations to show the range of a projectile launched at velocity, v, and angle, θ, is equal to

**Hint:** The velocity at the beginning and end of the motion has the same magnitude, but opposite direction.