Amodel rocket is launched straight upward with an initial speed of 52.1 m/s. it acceler- ates with a constant upward acceleration of 2.63 m/s2 until its engines stop at an altitude of 170 m. what is the maximum height reached by the rocket?

184.10 m

Explanation:

In order to solve this problem, we have to divide it into two parts:

a) When the rocket is moving with an acceleration

b) When the rocket is moving with an acceleration

is the initial speed from ground

is the upward acceleration due to the rocket's engines

is the height the rocket reaches with this acceleration

We have to find the "final speed" the rocket has when it reaches :

(1)

(2)

(3)

(4)

Then we have to find the time it took to the rocket to reach this velocity with the following equation:

(5)

(6)

(7)

(8)

At this point the acceleration is the acceleration due gravity () and the final velocity we calculated in equation (4) part a, is now the initial velocity in this part b:

On the other hand, it is known that in projectile motion (as this situation) the maximum height is when the velocity of the rocket is zero ().

So, we will use equation (1) again but with this new data:

(9)

Isolating :

(10)

(11)

Finally: