# 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?

###### FREE Expert Solution

Drag force on the ball is given by:

$\overline{){\mathbf{D}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{C}}{\mathbf{\rho }}{\mathbf{A}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

We'll also use Newton's second law:

$\overline{){\mathbf{\Sigma F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

This implies that:

D = ma = mg

The velocity of the ball is twice its terminal velocity.

$\begin{array}{rcl}{\mathbf{D}}_{\mathbf{2}{\mathbf{v}}_{\mathbf{\tau }}}& \mathbf{=}& \frac{\mathbf{1}}{\mathbf{2}}\mathbf{C}\mathbf{\rho }\mathbf{A}\mathbf{\left(}\mathbf{2}{\mathbf{v}}^{\mathbf{2}}\mathbf{\right)}\\ & \mathbf{=}& \mathbf{4}\mathbf{\left(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{C}\mathbf{\rho }\mathbf{A}{\mathbf{v}}^{\mathbf{2}}\mathbf{\right)}\end{array}$

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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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Drag Force & Terminal Velocity concept. If you need more Drag Force & Terminal Velocity practice, you can also practice Drag Force & Terminal Velocity practice problems.

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Based on our data, we think this problem is relevant for Professor Navarro Perez's class at SDSU.