Question

A pellet gun is fired straight downward from the edge of a cliff that is 25.2 m above the ground. The pellet strikes the ground with a speed of 30.4 m/s. How far above the cliff edge would the pellet have gone had the gun been fired straight upward?

Answer 1

Answer 2

Calculation:

1. Understand the Downward Scenario:

• Cliff height (h): 25.2 m

• Final speed (v): 30.4 m/s (downward)

• Gravity (g): 9.81 m/s²

2. Find Initial Speed (u) Using Kinematics:
   When fired downward:

   $$v^2=u^2+2gh$$

   Plug in:

   $$(30.4{)}^2=u^2+2(9.81)(25.2)$$$$924.16=u^2+494.424$$$$u^2=924.16-494.424=429.736$$$$u=\sqrt{429.736}\approx 20.73\text{m/s (initial speed)}$$

3. Calculate Maximum Height if Fired Upward:
   At max height, final speed $v=0$.

   $$0=u^2-2gH$$$$H=\frac{u^2}{2g}=\frac{(20.73{)}^2}{2\times 9.81}$$$$H\approx \frac{429.7}{19.62}\approx 21.6\text{m}$$

Short Answer:
The pellet would have reached 21.6 meters above the cliff if fired upward.