Question

If Michael Jordan has a vertical leap of $1.29m$, then what is his takeoff speed?
A) $5.03\text{ m/s}$
B) $5.3\text{ m/s}$
C) $4.03\text{ m/s}$
D) $7.03\text{ m/s}$

Answer 1

Hint: Vertical leap means a person jumps vertically upwards and reaches a maximum height. It is very similar to throwing a ball upwards, which will attain a particular height and then come down.

Complete step by step answer:
So the maximum height achieved from the jump is $1.29m$. The final velocity at the maximum height is zero. The acceleration acting on the body is the acceleration due to gravity acting against the motion of the body.
So according to Newton’s third equation of motion, we have,
${{v}^{2}}-{{u}^{2}}=2as$
Where,
v is the final velocity of the body.
u is the initial velocity of the body.
a is the acceleration on the body.
s is the displacement.
In our case $v=0,a=-g=-9.8m{{s}^{-2}},s=h=1.29m$.The minus sign on ‘g’ signifies the acceleration due to gravity is acting against the motion of the body. The final velocity (v) in our case is zero since the velocity of the body at the highest point is zero. Substituting these values in the equation, we get,
$0-{{u}^{2}}=2\left( -g \right)h$
$\Rightarrow {{u}^{2}}=2gh$
$\therefore u=\sqrt{2gh}$
$u=\sqrt{2\times 9.8m{{s}^{-2}}\times 1.29m}$
$\therefore u=5.03\text{ m/s}$
So the answer to the question is option (A)- $5.03\text{ m/s}$
Additional Information:
The vertical jump is an excellent way to measure the endurance and fitness of an athlete. It is also known as the Sargent jump.

Note:
The time taken by the body to reach the ground when dropped from a height h is given by
$t=\sqrt{\dfrac{2h}{g}}$
h is the height from which the ball is dropped
g is the acceleration due to gravity.
An object which is projected upwards is said to be in free fall even if it is moving upwards because gravity is the only force acting on it. So any kind of projectile motion can be considered as an example of free fall when excluding the factors like air friction and drag.