# 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?

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

###### 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

###### 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?

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 Force Problems with Motion concept. You can view video lessons to learn Force Problems with Motion. Or if you need more Force Problems with Motion practice, you can also practice Force Problems with Motion practice problems.

What professor is this problem relevant for?

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