A rocket is fired vertically upwards with initial velocity 92 m/s at the ground level. Its engines then fire and it is accelerated at 4m/s2 until it reaches an altitude of 1200 m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance.

The rocket above the ground is in 44 sec.

Explanation:

Given that,

Initial velocity = 92 m/s

Acceleration = 4 m/s²

Altitude = 1200 m

Suppose, How long was the rocket above the ground?

We need to calculate the time

Using equation of motion

Put the value into the formula

We need to calculate the velocity

Using equation of motion

Put the value into the formula

When the rocket hits the ground,

Then, h'=0

We need to calculate the time

Using equation of motion

Put the value into the formula

When the rocket is in the air it is the sum of the time when it reaches 1000 m and the time when it hits the ground

So, the total time will be

Hence, The rocket above the ground is in 44 sec.