Can someone help me find Delta Time for the first 150 meters of this question. Everytime I try and get it by using the quadratic formula I get two negative numbers which I don't think is right.

Question

A model rocket is launched straight upward with an initial speed of 50.0m/s. It accelerates with a constant upward acceleration of 2.00 m/s^2 until its engine stops at an altitude of 150m.

a)What is the maximum height reached by the rocket?
b)When does the rocket reach maximum height?
c)How long is the rocket in the air?
d)With what speed does the rocket hit the ground when it crashes.

Answer 1

d=vo*t +1/2 2 t^2
150=50t +t^2
t^2+50t-150=0

t= (50 +-sqrt (2500+4*1*150)/2

= (50 +- 55.7)/2= a minute.