Question

A ball is thrown up at 30m/s from the ground. What is it s maximum height?

How long did it take?

Answer 1

Maximum height reached by the ball thrown up at 30m/s is 3.06 seconds and the height reached is 45.9 meters

Explanation:

Given:

Initial velocity
`u=30 \mathrm{m} / \mathrm{s}`

To find :

maximum height =?

time taken=?

Solution:

Step 1:Finding the time taken to reach the highest point:

The velocity of the ball at its highest ,final velocity v=0

Using the formula,

`v=u+a t`

Where a is acceleration due to gravity.Its value is
`-9.8 m / s^(2)`

Substituting the values:

`0=30+(-9.8) t`

`-30=(-9.8) t`

`t=(30)/(9.8)`

`t=3.06 \mathrm{seconds}`

Step 2: finding the highest point

Using the formula

`v^(2)-u^(2)=2 a s`

where

s is the maximum highest.

Substituting values

`0^(2)-(30)^(2)=2(-9.8) s`

`0-900=(-19.6) s`

`-900=(-19.6) s`

`s=(900)/(19.6)`

`s=45.9 \text { meters }`

Result:

Thus the maximum height reached is 45.9 meters in 3.06 seconds

Answer 2

The maximum height of the ball is 45.92 meters

The time to reach the maximum height is 3.06 seconds

Step-by-step explanation:

A ball is thrown up at 30 m/s from the ground

We need to find its maximum height and how long it took

At maximum height speed equal zero

The acceleration of gravity is -9.8 m/s²

Lets find a rule contains distance, initial speed, final speed and

acceleration

→ v² = u² + 2 g h

where v is the final speed , u is the initial speed, g is the acceleration

of gravity and h is the height

→ v = 0 m/s , u = 30 m/s , g = -9.8 m/s²

Substitute these values in the rule above

→ (0)² = (30)² + 2(-9.8)(h)

→ 0 = 900 - 19.6 h

Add 19.6 h to both sides

→ 19.6 h = 900

Divide both sides by 19.6

→ h = 45.92 m

The maximum height of the ball is 45.92 meters

We need to find the time of the maximum height, then lets use the rule

→ v = u + g t

→ v = 0 m/s , u = 30 m/s , g = -9.8 m/s²

Substitute these values in the rule above

→ 0 = 30 - 9.8 t

Add 9.8 t to both sides

→ 9.8 t = 30

Divide both sides by 9.8

→ t = 3.06 seconds

The time to reach the maximum height is 3.06 seconds