At the start of his race, 86 kg 100-m dash champion Usain Bolt pushes against the starting block, exerting an average force of 1700 N. The force that the block exerts on his foot points 20 degrees above the horizontal. Determine his horizontal acceleration, and his horizontal speed after the force is exerted for 0.32s.

Question

At the start of his race, 86 kg 100-m dash champion Usain Bolt pushes against the starting block, exerting an average force of 1700 N.  The force that the block exerts on his foot points 20 degrees above the horizontal.  Determine his horizontal acceleration, and his horizontal speed after the force is exerted for 0.32s.

ameerry · Answer

for the first part we need to look at newtons third law of motion 
$$F=Ma$$
accourding to this we can fiur out our acceleration byputtin in our two know variables,
the mass and the force put on Usain by the block.

natuarly since Usain is puches 1700N on the block the block would push the same force back, but since it pushes it at a 20 degree angle we need to figure out the vertical and orizontal components of the vector(force).

if you draw it out you end up with the horizontal component being equal to 
$$\cos(20) * 1700$$

so we just input that into the equasion 

$$\cos(20) * 1700 = 86 * a$$
we devide both sides by 86 and we end up with a.

ameerry · Answer

as for the second part,
we can use the followin equasion
$$V = V _{0} + a * T$$

now the we know a we can just substitute 
$$V = 0 + a * 0.32$$