Questions: A cliff jumper runs off a 15 m high cliff. Rocks extend 3.0 m past the cliff bottom. We can ignore air resistance.

Transcript text: A cliff jumper runs off a 15 m high cliff. Rocks extend 3.0 m past the cliff bottom. We can ignore air resistance.

Solution

Solution Steps

Step 1: Analyze the vertical motion

The jumper falls under the influence of gravity. We can use the following kinematic equation to determine the time it takes to fall 15 meters:

y = v₀t + (1/2)at²

where:

y = -15 m (vertical displacement, negative since downwards)
v₀ = 0 m/s (initial vertical velocity)
a = -9.8 m/s² (acceleration due to gravity)
t = time (what we want to find)

Step 2: Calculate the time of flight

-15 = (0)t + (1/2)(-9.8)t² -15 = -4.9t² t² = 15/4.9 t = √(15/4.9) ≈ 1.75 s

Step 3: Analyze the horizontal motion

The horizontal motion is at a constant velocity (since air resistance is negligible). We can use the following equation:

x = vt

where:

x = horizontal displacement
v = horizontal velocity (assumed constant since he "runs" off the cliff)
t = time (calculated in step 2)

Final Answer

The jumper's trajectory shows they will land beyond the rocks since we know the time it takes to fall is approximately 1.75 seconds, and they travel horizontally during this period. The image shows the jumper moving horizontally at a constant velocity and vertically accelerating towards the ground until he lands past the rocks. Thus, he _will_ clear the rocks.

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