How far above the cliff edge would the pellet have gone had the gun been fired straight upward?

Question

Before working this problem, review Conceptual Example 15. A pellet gun is fired straight downward from the edge of a cliff that is 28.8 m above the ground. The pellet strikes the ground with a speed of 39.0 m/s.

Answer 1

Let:

u be the firing velocity of the gun,

v be the velocity with which the pellet strikes the ground,

h0 be the height of the cliff,

h1 be the height the pellet goes above the cliff when shot upwards,

g be the acceleration due to gravity.

When the gun is fired downwards:

v^2 = u^2 + 2g h0

u^2 = v^2 - 2g h0

When the gun is fired upwards:

0 = u^2 - 2g h1

u^2 = 2g h1

Equating the two values of u^2:

v^2 - 2g h0 = 2g h1

h1 = v^2 / 2g - h0.

= 39.0^2 / (2 * 9.81) - 28.8

= 48.7 m.