A model rocket is launched straight upward with an initial speed of 49.4 m/s. It acceler- ates with a constant

A model rocket is launched straight upward with an initial speed of 49.4 m/s. It acceler- ates with a constant upward acceleration of 2.37 m/s2 until its engines stop at an altitude of 190 m. What is the maximum height reached by the rocket? The acceleration of gravity is 9.81 m/s2. Answer in units of m

So there will be two legs to the motion of the rocket.
1. when it is accelerating to 190m
2. when only gravity is acting on it

For the first leg, we already know 190m is the height, but we need to find Vf because that will be the Vi in leg 2.
So our variables are:
d = 190m
Vi = 49.4m/s
a = 2.37m/s^2
Vf = ?

Vf^2 = Vi^2 + 2ad
Vf^2 = 49.4^2 + 2*2.37*190
Vf^2 = 2440.36 + 900.6
Vf^2 = 3340.96
Vf = 57.8m/s

This will be the Vi in the second leg.
Variables for leg 2:
Vi = 57.8m/s
Vf = 0m/s
a = -9.8m/s^2
d = ?

Vf^2 = Vi^2 + 2ad
0^2 = 57.8^2 + 2*-9.8*d
0 = 3340.84 -19.6d
-3340.84 = -19.6d
170.45m = d

Now you add the two distances together to find the maximum height.

190m + 170.45m
= 360.45m

Therefore, the maximum height reached by the rocket is 360.45m.

Hope this helped!