You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 19 m/s2. After 23 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect any effects due to air resistance.)

What is the highest point your rocket reaches?

Determine the total time the rocket is in the air.

Find the speed of the rocket just before it hits the ground.

the first question could be answered by a similar question I answered:

http://www.jiskha.com/display.cgi?id=1284864933

try attempting the other questions on your own. repost with your work for further assistance.

To determine the highest point your rocket reaches, we can use the equation of motion for an object in freefall after the engine shuts off.

The equation for the displacement of an object under constant acceleration is given by:
s = ut + (1/2)at^2

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

Since the rocket is launched vertically with an initial velocity of 0 m/s, the equation simplifies to:
s = (1/2)at^2

Given that the upward acceleration is 19 m/s² and the time after the engine shuts off is 23 s, we can substitute these values into the equation:
s = (1/2)(19)(23)^2

Calculating this equation, we find that the rocket reaches a height of 11,089.5 meters or approximately 11.1 kilometers.

To determine the total time the rocket is in the air, we need to find the time it takes for the rocket to reach its maximum height and then double that time.

The time it takes for the rocket to reach its maximum height can be found using the equation:
v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Since the rocket is in freefall after the engine shuts off, the final velocity at the highest point is 0 m/s. The initial velocity is given as 0 m/s, and the acceleration is -9.8 m/s² (due to gravity). Substituting these values into the equation, we can solve for time:
0 = 0 + (-9.8)(t)

Solving for t, we find t = 0 s.

Doubling the time it takes for the rocket to reach its maximum height gives us the total time the rocket is in the air, which is:
2(23 s) = 46 s.

Therefore, the total time the rocket is in the air is 46 seconds.

To find the speed of the rocket just before it hits the ground, we can use the equation of motion:
v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Since the final velocity at the ground is 0 m/s, the initial velocity is the velocity of the rocket just before it hits the ground, the acceleration is -9.8 m/s² (due to gravity), and the time is the total time the rocket is in the air which is 46 seconds. Substituting these values into the equation, we can solve for the initial velocity:
0 = u + (-9.8)(46)

Solving for u, we find u = 451.6 m/s (rounded to one decimal place).

Therefore, the speed of the rocket just before it hits the ground is approximately 451.6 meters per second.