Question

Billy, a mountain goat, is rock climbing on his favorite slope one sunny spring morning when a rock resting on a ledge 40.0 m above falls toward him. How long does Billy have to duck and avoid injury? (Hint: What causes the rock to fall downward?)

a) 2.02 s
b) 4.04 s
c) 5.10 s
d) 6.08 s

Answer 1

Billy, the mountain goat, has approximately 2.86 seconds to move out of the way to avoid getting injured by the falling rock from a height of 40.0 meters.

Step-by-step explanation:

The student is asking how long it takes for a rock to fall from a ledge 40.0 m above the ground. The rock falls due to the force of gravity, and we can use the formula for the time of free fall under gravity to answer this question. The formula is t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (approx. 9.81 m/s²). Plugging in the numbers, we get:

t = √(2*40.0/9.81) = √(8.15) ≈ 2.86 s

Therefore, Billy, the mountain goat, has approximately 2.86 seconds to move out of the way to avoid injury.