Question

A ball, with a mass of 5.9kg, is thrown directly upwards. It reaches a maximum height of 10m from the point at which it was released.
Using the principle of energy conservation, and ignoring air resistance, calculate the ball's speed when it was released, in m/s.

Use a gravitational acceleration value of g = 9.8 m/s^2.

Answer 1

Answer:

14 m/s

Explanation:

We can solve the problem by using the law of conservation of energy.

At the beginning, when the ball is thrown from the ground, it has only kinetic energy, which is given by

$K=\frac{1}{2}mv^2$

where m = 5.9 kg is the mass of the ball and v is its initial speed.

As the ball goes up, its speed decreases, so its kinetic energy decreases and converts into gravitational potential energy. When the ball reaches its maximum height, the speed has become zero, and all the kinetic energy has been converted into gravitational potential energy, given by:

$U=mgh$

where g = 9.8 m/s^2 is the gravitational acceleration and h = 10 m is the maximum height reached by the ball.

Since we can ignore air resistance, energy must be conserved, so the initial kinetic energy must be equal to the final potential energy of the ball, so we can write:

$K=U\\\frac{1}{2}mv^2=mgh$

And we can solve the equation to find v, the initial speed of the ball:

$v=\sqrt{2gh}=\sqrt{2(9.8 m/s^2)(10 m)}=14 m/s$