Please provide detailed explanation. While moving between a tall tree and a buil

Question

Please provide detailed explanation.

While moving between a tall tree and a building, a squirrel drops an acorn straight down. A conveniently placed sensor on the ground determines the final velocity of the acorn before it hits the ground is 20m/s.

A.) Assuming air resistance is negligible, from what height did the acorn fall?

B.) How long did it take the acorn to reach the ground?

C.) If the acorn started its fall with an initial horizontal velocity, how would the time to fall compare to what you calculated in part B? Explain.

Explanation / Answer

A) Apply conservation of Energy

Initial PE = final KE

m*g*h = 0.5*m*v^2

h = v^2/(2*g)

= 20^2/(2*9.8)

= 20.4 m

B) Use kinemtaic equation,

vy = voy + g*t

20 = 0 + 9.8*t

t = 20/9.8

= 2.04 s

C) The time taken to fall down would be same. i.e 2.04 s

Time taken to fall down depends only on y-component of initial velocity.

t = (vy - voy)/g

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