Problem: A ball is shot from a compressed air gun at twice its terminal speed.a)What is the ball's initial acceleration, as a multiple of g, if it is shot straight up?b) What is the ball's initial acceleration, as a multiple of g, if it is shot straight down?

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FREE Expert Solution

Drag force on the ball is given by:

D=12CρAv2

We'll also use Newton's second law:

ΣF=ma

This implies that:

D = ma = mg

The velocity of the ball is twice its terminal velocity.

D2vτ=12CρA(2v2)=4(12CρAv2)

D2v = 4D = 4mg

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Problem Details

A ball is shot from a compressed air gun at twice its terminal speed.


a)What is the ball's initial acceleration, as a multiple of g, if it is shot straight up?
b) What is the ball's initial acceleration, as a multiple of g, if it is shot straight down?

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Based on our data, we think this problem is relevant for Professor Kulyk's class at UCF.