# A ball of mass 4 kg is thrown straight up in the earth's gravitational field with an initial...

## Question:

A ball of mass 4 kg is thrown straight up in the earth's gravitational field with an initial speed v0 = 14 m/s. a) What is the initial kinetic energy of the ball?How much work does the gravitational force do on the ball if it goes up to a height h = 1.9 m?What is the speed of the ball at a height h = 1.9 m?

## Energy conservation

We know that from the law of energy conservation that energy can neither be created nor be destroyed it can only change its forms from one to another. Therefore, the total energy of the system would remain constant at every instant.

Given

Mass of the ball (m) = 4 kg

The initial speed of the ball (u) = 14 m/s

(a)

The initial kinetic energy of the ball is given by

{eq}\displaystyle K = 0.5mu^{2} \\ K = 0.5*4*14^{2} \\ K = 392 \ J {/eq}

(b)

Now the work done by the gravitational field is given by gravitational potential energy

{eq}\displaystyle W = mgh \\ W = 4*9.81*1.9 \\ W = 74.56 \ J {/eq}

(c)

Now the energy at the height is given by

{eq}\displaystyle E = ( 0.5mv^{2}) + mgh {/eq}

Now applying the energy conservation

{eq}\displaystyle K = (0.5mv^{2}) + mgh \\ 392 = (0.5*4*v^{2}) + 74.56 \\ v = 12.598 \ m/s {/eq}