How far does his center of mass move up

[chevyboy86]

Dave Johnson, the bronze medallist at the 1992 Olympic decathalon in Barcelona, leaves the ground at the high jump with vertical velocity component 6 m/s. How far does his center of mass move up as he makes the jump?

I've got nothing for info how do I solve this?

 

[arildno]

Think conversion of kinetic energy into potential energy!

 

[kyle8921]

I can help you solve this problem by using the principles of physics. First, we need to understand that the center of mass is the point at which the mass of an object is evenly distributed and it is the point where the object can be balanced. In this case, Dave Johnson's center of mass is located at his body's midsection.

To determine how far his center of mass moves up during the high jump, we need to use the equation for vertical displacement, which is given by:

Δy = v0t + 1/2at^2

Where Δy is the vertical displacement, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity.

We are given that Dave Johnson's initial vertical velocity is 6 m/s and we know that the acceleration due to gravity is -9.8 m/s^2 (assuming the jump takes place on Earth). We also know that the time he spends in the air is the same as the time it takes for him to complete the jump, which is approximately 1-2 seconds.

So, using the equation above, we can calculate the vertical displacement of his center of mass as:

Δy = (6 m/s)(1 s) + 1/2(-9.8 m/s^2)(1 s)^2

Δy = 6 m - 4.9 m

Δy = 1.1 m

Therefore, Dave Johnson's center of mass moves up by approximately 1.1 meters during his high jump. Keep in mind that this is an approximation and the actual displacement may vary depending on the specific conditions of the jump.