A person reaches a maximum height of 65cm when jumping straight up from a crouched position. During the jump itself, the person's body from the knees up rises a distance of around 50cm . To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump.

With what initial speed does the person leave the ground to reach a height of 65cm ?
I found this to be 3.6 m/s which is correct.

In terms of this jumper's weight W , what force does the ground exert on him or her during the jump?

I'm not sure how to start this, I've attempted a few ways and each has been wrong.

I figured the answer out, but for future reference for others:

F = reaction of the ground
F = mg + ma

V² = 2ax (x = 0.50m)
a = V²/2x = 2gh/2x = gh/x
F = mg + mgh/x
F = W + Wh/x
F = W(1+h/x)
here
F = (1 + 0.64/0.50)W
F = 2.3W

Well, it seems like this jumper really wants to defy gravity! Now, to answer your question about the force exerted by the ground, let's think about it in a fun and humorous way.

Imagine the ground as a trampoline, and our jumper as a really bouncy clown. When the clown jumps on the trampoline, it exerts a force on the trampoline, and the trampoline bounces the clown back up. Similarly, when our jumper leaves the ground, the ground pushes back with a force to propel the jumper upwards.

Now, since we are talking about force, we know that it is related to weight. So, the force exerted by the ground on our jumper during the jump is equal to the jumper's weight, which is W.

So, the ground exerts a force on our intrepid jumper that is equal to their weight. And just like a clown soaring through the air, the jumper experiences this force as they reach for the sky!

Hope that brings a smile to your face!

To find the force exerted by the ground on the jumper during the jump, you can use the principle of conservation of energy.

Since the jumper reaches a maximum height of 65 cm, the potential energy at this height is equal to the initial kinetic energy.

The potential energy at a height h is given by the equation:

Potential Energy = m * g * h,

where m is the mass of the jumper, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (converted to meters).

The initial kinetic energy is given by the equation:

Initial Kinetic Energy = (1/2) * m * v^2,

where v is the initial velocity of the jumper.

Since the potential energy at the maximum height is equal to the initial kinetic energy, we can set up the following equation:

m * g * h = (1/2) * m * v^2.

Substituting the given values, we have:

(1/2) * m * (3.6)^2 = m * 9.8 * 0.65.

Simplifying the equation, we get:

(1/2) * (3.6)^2 = 9.8 * 0.65.

Solving for the value of m, we find:

m = (2 * 9.8 * 0.65) / (3.6)^2.

Now that we have the mass m, we can calculate the force exerted by the ground using Newton's second law, which states that Force = mass * acceleration. In this case, the acceleration is equal to the acceleration due to gravity.

Force = m * g.

Substituting the values, we find:

Force = [(2 * 9.8 * 0.65) / (3.6)^2] * 9.8.

Evaluating this expression will give you the force exerted by the ground on the jumper during the jump.

To find the force exerted by the ground on the jumper during the jump, we can utilize Newton's laws of motion.

The force exerted by the ground on the jumper is equal to the jumper's weight, W, which can be calculated using the equation W = mg, where m is the mass of the jumper and g is the acceleration due to gravity (approximately 9.8 m/s²).

Given that the jumper's weight is W, we need to determine the mass of the jumper to find the value of W. However, this information is not provided in the question. Without the mass of the jumper, it is not possible to directly calculate the force exerted by the ground.

If the mass of the jumper were provided, we could calculate the force exerted by multiplying the mass by the acceleration due to gravity. However, since the mass is unknown in this case, we cannot find the exact force value.