Question

A 1-lb stone is heaved vertically upward with a speed of 40 ft/s from the top of a 100-ft cliff, and it hits the water below 100-ft below (narrowly missing the thrower on the way down). WATCH YOUR UNITS!! Find the stone's
a) Total energy at time zero (set PE=0 at the water level).

Answer 1

first find out how high it goes up before it stops (when it has no kinetic energy. Original height is 200 above water.
v = Vi - 32 t
0 = 40 - 32 t
t = 5/4 sec

h = 200 + 40 t - 16 t^2
h = 200 + 40(5/4) - 16(25/16)
h = 200 + 50 - 25
h = 225 feet stopped above the water
Now
PE = m g h = 1 * 225 = 225 foot pounds
that is the total energy since it is not moving up there.