A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 87.9 m/s2 for 1.51 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?

See previous post: Wed, 8-12-15, 12:14 AM.

To find the maximum altitude reached by the rocket, we can use the kinematic equation for displacement:

Δy = v1*t + (1/2)*a*t^2

Where:
Δy is the displacement (maximum altitude)
v1 is the initial velocity (since the rocket starts from rest, v1 will be 0)
t is the duration of acceleration (1.51 seconds)
a is the constant acceleration (87.9 m/s^2)

Substituting the given values into the equation, we get:

Δy = 0*(1.51) + (1/2)*(87.9)*(1.51^2)
= 0 + 0.5*87.9*(2.2801)
= 0 + 0.5*87.9*2.2801
≈ 0 + 100.84095
≈ 100.84095 meters

Therefore, the rocket will reach a maximum altitude of approximately 100.84095 meters above the ground.