2-objects, 2-dimensions: A firefighter is standing still watching a cat which is

Question

2-objects, 2-dimensions: A firefighter is standing still watching a cat which is hanging from its claws 13.5 meters up on a tree branch. The firefighter is not directly under the cat, but 5.00 meters away horizontally. At the instant the cat loses its grip and starts to fall, the firefighter goes in motion with acceleration aFF and gets there just in time, catching the cat 1.6 meters above the ground. Assuming that aFF was constant, what was it’s value so that the firefighter was exactly able to catch the cat that way?

Explanation / Answer

here,

h1 = 13.5 m , h2 = 1.6 m

let the time taken be t

h1 - h2 = 0 + 0.5 * g * t^2

13.5 - 1.6 = 0 + 0.5 * 9.81 * t^2

solving for t

t = 1.56 s

let the accelration of firefighter be aFF

5 = 0 + 0.5 * aFF * t^2

5 = 0 + 0.5 * aFF * 1.56^2

solving for aFF

aFF = 4.1 m/s^2

the accelration of firefighter is 4.1 m/s^2

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