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?