A carnival game has players hit a pad with a large rubber mallet. This fires a ball up 20-foot vertical chute towards a target at the top. A prize is awarded if the ball hits the target. Explain how to find the initial volocities in feet per second for which the ball will fail to hit the target. The height is modeled by the function h(t)=-16t²+vt, where v is the initial velocity.
from physics ... kinetic energy at the bottom = potential energy at the top
1/2 m v^2 = m g h ... v^2 = 2 g h = 2 * 32 ft/s^2 * 20 ft = 1280 ft^2/s^2
... m is the mass of the ball (which cancels)
... g is gravitational acceleration ... 32 ft/s^2
find v ... the ball will fail to hit the target for any value less than this