Question

A boy throws a ball up into the air with a speed of 8.2 m/s. The ball has a mass of 0.3 kg. How much gravitational potential energy will the ball have at the top of its flight? (Assume there is no air resistance

Answer 1

10.1 J

Hope this helped!

Step-by-step explanation:

Answer 2

We can use the law of conservation of energy to solve the problem.

The total mechanical energy of the system at any moment of the motion is:

`E=U+K = mgh + (1)/(2)mv^2`
where U is the potential energy and K the kinetic energy.

At the beginning of the motion, the ball starts from the ground so its altitude is h=0 and therefore its potential energy U is zero. So, the mechanical energy is just kinetic energy:

`E_i = K_i = (1)/(2)mv^2 = (1)/(2)(0.3 kg)(8.2 m/s)^2=10.09 J`

When the ball reaches the maximum altitude of its flight, it starts to go down again, so its speed at that moment is zero: v=0. So, its kinetic energy at the top is zero. So the total mechanical energy is just potential energy:

`E_f = U_f`
But the mechanical energy must be conserved, Ef=Ei, so we have

`U_f = K_i`
and so, the potential energy at the top of the flight is

`U_f = K_i = 10.09 J`