# A model rocket is fired vertically from rest. It has a constant acceleration of 17.5m/s^2 for the first 1.5 s. Then its fuel is exhausted, and it is in free fall. (a) Ignoring air resistance, how high does the rocket travel? Cont.

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(b) How long after liftoff does the rocket return to the ground?

(b) How long after liftoff does the rocket return to the ground?

##### 1 Answer

(a) Given acceleration

Inserting given values we get

Using the following kinematic equation for finding height attained till

These equations (2) and (3) give initial conditions for the freely falling rocket after fuel is exhausted.

Let rocket reach a maximum height

To calculate height

Maximum height attained is

(b) Let time taken to travel from height

It can be found from the kinematic equation (1)

Now for downward journey of rocket, let the time taken for falling from maximum height to the ground be

Acceleration due to gravity is in the direction of motion. We have

Total time taken after liftoff

-.-.-.-.-.-.-.-.-.-.-.

Alternate method for part (b)

After

Displacement

Time taken to reach ground can be calculated using (4). Acceleration due to gravity acting against the direction of motion.

Roots of this quadratic can be found using

Using inbuilt graphic tool.

Ignoring the negative root as time can not be negative. we have

Time of flight

Total time taken after liftoff