Question

A ball is dropped from rest. After time t the ball has travelled a distance of x. After time 5t the ball has travelled a distance of?

Answer 1

The ball traveled 25x after 5t

Answer 2

Given:

Distance travelled after time t = x

Given that the ball was dropped from rest, let's find the distance the ball travelled after time 5t.

To find the distance, apply the motion formula:

`h=(1)/(2)*gt^2`

Where:

g is the acceleration due to gravity = 9.8 m/s²

h is the vertical distance travelled.

t is the time.

After time t, we have:

`x=(1)/(2)gt^2`

After time 5t, we have:

`h=(1)/(2)g(5t)^2`

Now divide the second expression by the first expression.

`\begin{gathered} ((1)/(2)g(5t)^2)/((1)/(2)gt^2) \\ \\ ((5t)^2)/(t^2) \\ \\ =(5^2t^2)/(t^2) \\ \\ =(25t^2)/(t^2) \\ \\ =25 \end{gathered}`

Therefore, after the time 5t, the ball has travelled a distance of 25x.

• ANSWER:

25x