A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 86.9 m/s2 for 1.69 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?

about 15 meters?

To find the maximum altitude reached by the rocket, we can use the equations of motion for uniformly accelerated motion.

First, we need to determine the velocity of the rocket when its fuel runs out. We can use the equation:

v = u + at

Where:
v is the final velocity (unknown)
u is the initial velocity (0 m/s, since the rocket starts from rest)
a is the acceleration (86.9 m/s^2)
t is the time (1.69 seconds)

Substituting the given values into the equation:

v = 0 + (86.9 m/s^2)(1.69 s)
v = 146.761 m/s

Now, we can use this final velocity to find the maximum altitude. We can use the equation:

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

Where:
s is the distance traveled in the given direction (unknown, maximum altitude in this case)
u is the initial velocity (0 m/s, since the rocket starts from rest)
a is the acceleration (86.9 m/s^2)
t is the time (1.69 seconds)

Substituting the values into the equation:

s = (0 m/s)(1.69 s) + (1/2)(86.9 m/s^2)(1.69 s)^2
s = 0 + (1/2)(86.9 m/s^2)(2.8561 s^2)
s = 73.627 m

Therefore, the maximum altitude reached by the rocket is 73.627 meters above the ground.