How Do You Calculate Initial Velocity from Jump Height?

[btr94]

Homework Statement

Standing position: 100cm
Lowered hip position: 77cm
Peak height: 140cm

Question "Use the peak height of the jump and the standing hip position to calculate the initial velocity of the jumper just after he left the ground"

Homework Equations

Unknown

The Attempt at a Solution

Unknown - I only know equations that require time. I know no time measurement in this problem.

The problem is a jumping problem. The variable above, in order, are:
1. Standing tall - from the floor to the hip
2. Crouched down to jump - from the floor to the hip
3. In mid-air at the peak of the jump - from the floor to the hip.

These were measured using a 2-meter stick.

 

[aimslin22]

You need to use the force formulas:

PE spring = 1/2kx^2
KE = 1/2mv^2

 

[thomate1]

To calculate the initial velocity of the jumper, we can use the equation for projectile motion: h = vi^2sin^2(theta)/2g, where h is the peak height, vi is the initial velocity, theta is the angle of the jump, and g is the acceleration due to gravity.

In this case, we can assume that the angle of the jump is 90 degrees, since the jumper is jumping straight up. Also, we know that the acceleration due to gravity is 9.8 m/s^2.

Using the given values, we can plug them into the equation and solve for vi:

140cm = vi^2sin^2(90)/2(9.8)

Converting all units to meters, we get:

1.4m = vi^2(1)/19.6

Solving for vi, we get:

vi = √(1.4*19.6)

vi = 4.2 m/s

Therefore, the initial velocity of the jumper just after leaving the ground is 4.2 m/s.