Homer Hickham and his buddies launched model rockets in the late 1950's when the US was trying to get a rocket into space. If homer launches a rocket from rest and its engine delivers a constance acceleration of 8.2 m/s^2 for 5.0seconds after which the fuel is used up by the rocket.

A) Find the maximum altitude reached by the rocket.

B) Find the total time the rocket is in flight (up and down)

during burn:

v = 8.2t
v(5) = 41 m/s
h = 1/2 (8.2) t^2
h(5) = 102.5 m

So, after 5 seconds, the rocket is 102.5 meters up, with a speed of 41.0 m/s.

Now, only gravity provides acceleration, so

h = 102.5 + 41.0t - 4.9 t^2
h=0 when t = 10.382

max h when t = -41.0/-9.8 = 4.18
h(4.18) = 188.265

So, the rocket reaches a max height of 188.27m after 4.18 seconds of ballistic flight, and hits the ground again after 5.0+10.382 = 15.382 seconds have elapsed.

To find the maximum altitude reached by the rocket (A), we need to use the kinematic equation for displacement. Here's how to calculate it:

Step 1: Find the initial velocity (Vi) of the rocket. Since it is launched from rest, Vi = 0 m/s.

Step 2: Find the time the rocket is in motion until the fuel runs out. The given time is 5.0 seconds.

Step 3: Use the equation s = Vi * t + (1/2) * a * t^2 to calculate the displacement, where s is the displacement, Vi is the initial velocity, t is the time, and a is the acceleration.

Plugging in the values:
s = 0 * 5.0 + (1/2) * 8.2 * (5.0)^2
s = 0 + (1/2) * 8.2 * 25
s = 102.5 meters

Therefore, the maximum altitude reached by the rocket is 102.5 meters.

To find the total time the rocket is in flight (up and down) (B), we need to consider that the rocket goes up for a certain time and comes down for the same amount of time.

Step 1: Since the time taken for the rocket to reach its maximum altitude is 5.0 seconds, we know that the total time in flight is twice that.

Total time = 2 * 5.0 seconds
Total time = 10.0 seconds

Therefore, the total time the rocket is in flight (up and down) is 10.0 seconds.