We're asked to find the** ****acceleration** and the **speed** that results.

This problem is about forces in a **vertical plane**. Like with any forces problems, we'll follow the same series of steps:

- Draw a
**free body diagram (FBD)**, making sure to include and labe￼l coordinate axes - Set up Newton's Second Law equation (
**∑***F*=)**ma** **Solve**for the target variable

The equations to convert between components and magnitude-angle notation will always be useful when we're dealing with forces at different angles—

Calculating components: $\overline{)\begin{array}{rcl}{\mathit{F}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{\theta}\\ {\mathit{F}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{\theta}\end{array}}$

Calculating magnitude: $\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{F}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{F}}_{\mathit{y}}}^{\mathbf{2}}}}$

Calculating angle: $\overline{){\mathbf{tan}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{F}}_{\mathit{y}}}{{\mathit{F}}_{\mathit{x}}}}$

For this problem, we'll also need to remember the equation for a constant or average acceleration:

$\overline{){\mathit{a}}{\mathbf{=}}\frac{\mathbf{\u2206}\mathit{v}}{\mathbf{\u2206}\mathit{t}}}$

At the instant a race began, a 66-kg sprinter exerted a force of 987 N on the starting block at a 41° angle with respect to the ground.

(*a*) What was the horizontal acceleration of the sprinter?

(*b*) If the force was exerted for 0.36 s, with what speed did the sprinter leave the starting block?

Frequently Asked Questions

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 Forces in 2D concept. You can view video lessons to learn Forces in 2D. Or if you need more Forces in 2D practice, you can also practice Forces in 2D practice problems.