Question

Billy, a mountain goat, is rock climbing on his favorite slope one sunny spring
morning when a rock comes hurtling toward him from a ledge 40.0 m above.
Billy ducks and avoids injury. a) How fast is the rock traveling when it passes
Billy?

Answer 1

Answer on Question 62462, Physics – Mechanics | Relativity

Question:

Billy, a mountain goat, is rock climbing on his favorite slope one sunny spring morning when a rock comes hurtling toward him from a ledge 40.0 m above. Fortunately, Billy ducks and avoids injury.

a) How fast is the rock traveling when it passes Billy?

Solution:

We can find the final velocity of the rock from the kinematic equation:

$$v _ {f} ^ {2} = v _ {i} ^ {2} + 2 a h,$$

here, $v_{i} = 0 \frac{m}{s}$ is the initial velocity of the rock, $a = g = 9.8 \frac{m}{s^2}$ is the acceleration due to gravity (we take the downwards to be the positive direction, thus the acceleration due to gravity will be positive) and $h$ is the height.

Then, we can calculate the final velocity of the rock (when it passes Billy):

$$v _ {f} = \sqrt {2 g h} = \sqrt {2 \cdot 9 . 8 \frac {m}{s ^ {2}} \cdot 4 0 . 0 m} = 2 8 \frac {m}{s}.$$

Answer:

a) $v_{f} = 28 \frac{m}{s}$.

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