A model rocket is launched straight upward with an initial speed of 47.7 m/s. It accelerates with a constant upward acceleration of 2.02 m/s2 until its engines stop at an altitude of 157 m. What is the maximum height reached by the rocket?

How long after lift off does the rocket reach its maximum height?

How long is the rocket in the air?

I found the answer to the first question but I don't know how to get the second and third question. Help?

http://www.jiskha.com/display.cgi?id=1390518679

Sure! I can help you with that.

To find how long after lift off the rocket reaches its maximum height, you can use the kinematic equation for displacement:

s = ut + (1/2)at^2

Where:
s = displacement
u = initial velocity
a = acceleration
t = time

In this case, the initial velocity is 47.7 m/s, the acceleration is -2.02 m/s^2 (negative because the rocket is decelerating), and the displacement is the maximum height, which you need to find.

Since the rocket is reaching its maximum height, its final velocity at this point is 0 m/s. Therefore, using the equation:

0 = 47.7 - 2.02t

Rearranging the equation, we find:

2.02t = 47.7
t = 47.7 / 2.02

t ≈ 23.6 seconds

So, the rocket reaches its maximum height approximately 23.6 seconds after lift off.

Now, to find how long the rocket is in the air, we need to consider the entire duration of the flight. The rocket starts from rest and reaches its maximum height before it starts falling back down. The total time in the air is twice the time it takes for the rocket to reach its maximum height.

So, the total time in the air is:

2 * 23.6 ≈ 47.2 seconds

Therefore, the rocket is in the air approximately 47.2 seconds in total.