# Problem: 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?

###### FREE Expert Solution

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:

1. Draw a free body diagram (FBD), making sure to include and labe￼l coordinate axes
2. Set up Newton's Second Law equation ( ma )
3. 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:

Calculating magnitude: $\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbit{F}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbit{F}}_{\mathbit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{F}}_{\mathbit{y}}}^{\mathbf{2}}}}$

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

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

$\overline{){\mathbit{a}}{\mathbf{=}}\frac{\mathbf{∆}\mathbit{v}}{\mathbf{∆}\mathbit{t}}}$

###### Problem Details

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?