Question

A stone is thrown vertically up from the ground. It reaches a maximum height of 150 m in 5 seconds. Determine the velocity with which the stone is thrown upward.

Answer 1

Given:

Maximum height = 150 m

Time it takes to reach naximum height = 5 seconds.

Let's find the velocity with which the stone is thrown upward.

To find the velocity, apply the formula:

`x=ut+(1)/(2)at^2`

Where:

• u is the initial velocity (velocity with which the stone is thrown upward)

,

• a is acceleration due to gravity = 9.8 m/s²

,

• x is the maximum height = 150 m

,

• t is the time.

At the maximum height, the final velocity is 0 m/s.

Thus, we have:

`150=5u+(1)/(2)*9.8*5^2`

Let's solve for u.

We have:

`\begin{gathered} 150=5u+4.9*25 \\ \\ 150=5u+122.5 \\ \\ 5u=150-122.5 \\ \\ 5u=27.5 \end{gathered}`

Divide both sides by 5:

`\begin{gathered} (5u)/(5)=(27.5)/(5) \\ \\ u=5.5\text{ m/s} \end{gathered}`

Therefore, the velocity with which the stone is thrown upward is 5.5 m/s.

ANSWER:

5.5 m/s