Question

The standing vertical jump is a good test of an athlete's strength and fitness. The athlete goes into a deep crouch, then extends his legs rapidly; when his legs are fully extended, he leaves the ground and rises to his highest height. It is the force of the ground on the athlete during the extension phase that accelerates the athlete to the final speed with which he leaves the ground. A good jumper can exert a force on the ground equal to twice his weight. If his crouch is 55 cm deep, how far off the ground does he rise?

Answer 1

Answer:

The athlete will rise 1.10 meters off the ground

Explanation:

Vertical Motion

If an object is launched vertically upwards at an initial speed vo, then it will reach a maximum height given by

$\displaystyle y_m=\frac{v_o^2}{2g}$

The athlete can exert a net force upwards equal to twice his weight. It makes him accelerate upwards at

$\displaystyle a=\frac{F_n}{m}=\frac{2W}{m}=2g$

The speed at the end of his push can be computed by

$v^2=2ay$

Replacing the value of a obtained above:

$v^2=4gy$

where y is the length of this crouch

$v^2=4\cdot 9.8\cdot 0.55$

$v=4.64\ m/s$

This is the initial speed of this vertical launch, thus

$\displaystyle y_m=\frac{4.64^2}{2\cdot 9.8}$

$y_m=1.10\ m$