Amazing Kangaroo Jumping Energy Calculation

How high can a kangaroo jump with a mass of 90 kg and an initial velocity of 5 m/s?

Calculate the maximum gravitational energy of the kangaroo when it reaches its highest point.

Answer:

The maximum gravitational energy of the kangaroo with a mass of 90 kg, jumping with an initial velocity of 5 m/s and reaching its highest point is 1125 J.

When a kangaroo of mass 90 kg jumps with an initial velocity of 5 m/s, it reaches its maximum gravitational energy when it reaches its highest point. To calculate this maximum gravitational energy, we use the formula:

U = mgh

Where: U is the gravitational potential energy, m is the mass of the kangaroo (90 kg), g is the acceleration due to gravity (9.8 m/s²), h is the height reached by the kangaroo.

First, we need to calculate the height h reached by the kangaroo:

Using the kinematic equation: v² = u² + 2as where: initial velocity (u = 5 m/s), final velocity at highest point (v = 0), acceleration due to gravity (a = -9.8 m/s²).

Substitute the values and solve for s: 0 = 5² + 2(-9.8)s 0 = 25 - 19.6s 19.6s = 25 s = 1.28 m

Now, we calculate the maximum gravitational energy U:

U = mgh = 90 * 9.8 * 1.28 = 1125 J

Therefore, the maximum gravitational energy of the kangaroo when it reaches its highest point is 1125 J.