Purpose: To predict the landing point of a projectile after it has rolled down a ramp.
Equipment needed: Each group needs: a ramp, target paper, carbon paper, meter stick, and plumb line.
Background
Remember that when analyzing twodimensional projectile motion, the horizontal and vertical motions are independent of each other. Horizontally, projectiles in freefall travel at a constant velocity; while vertically, they experience uniform acceleration resulting in a classic parabolic trajectory. Our secret to working projectile problems was to build a chart in which we delineated the Horizontal  Vertical properties in each situation.
Horizontally, the only equation available to us was R = v_{H}t, where v_{H} represents the projectile's constant horizontal velocity. Vertically, in the above illustration, the projectile's initial velocity equaled zero, since it was launched straight forward. Usually, in this situation, we let v_{o} = 0, a = 9.8 m/sec^{2}, and s = h and then used the kinematics equation s = v_{o}t + ½at^{2} to solve for the time that the projectile spent in the air.
Your goal in this experiment is to predict where a steel ball will land on the floor after having rolled down an incline plane. The final test of your measurements and computations will be to position a bull'seye on the floor so that the ball lands in its center circle on the first attempt. Make sure that ALL measurements and calculations are reported with three significant figures.
Part I: The Experiment
Step 1: Assemble your ramp. Make it as sturdy as possible so the steel ball bearing rolls smoothly and consistently. The ramp should not sway or bend. Since the ball bearing must leave the table horizontally, make sure that the horizontal part of the ramp is level with the surface of the table. The vertical height, h, of the ramp should be no less than 7 cm.
Step 2: Calculate the ball bearing's horizontal velocity at the base of the ramp using conservation of energy principles. At the top of the ramp, if the ball bearing is released from rest, it will only have potential energy, PE, which equals the product of its mass (in kilograms) times the acceleration due to gravity (9.8 m/sec^{2}) and its height (in meters) above an arbitrary reference line. At the base of the ramp, the ball has both translational kinetic energy, KE = ½mv^{2}, and rotational kinetic energy, KE_{rot} = ½Iw^{2}. Recall that the moment of inertia for a solid sphere equals I = (2/5)mr^{2} and that v = rw.

PE_{top} = Total KE_{base} mgh = ½mv^{2} + ½Iw^{2}

This velocity at the base of the incline will remain the ball bearing's horizontal velocity when it leaves the table. Remember that you will need to release the ball at the very top of the ramp and not put any pressure against the ramp that might result in it "springing" forward when the ball is released.

Step 4: Using the appropriate equation from the background information given above, calculate the time, t, that the ball bearing will take to fall from the base of the ramp on the table's surface to the floor.
t (in sec) = 
Step 5: The range is the horizontal distance a projectile once it is leaves the table until it strikes the floor. Calculate the range of the ball bearing. Show your equation and any necessary calculations used in predicting the ball's range.
R (in m) = 
