A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 90.3 m/s2 for 1.75 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 need to use the kinematic equation for motion in one dimension:
\[ h = h_0 + v_0 \cdot t + \frac{1}{2} \cdot a \cdot t^2 \]
where,
- h is the maximum altitude (height) reached by the rocket.
- h_0 is the initial height, which is 0 in this case as the rocket starts from the ground.
- v_0 is the initial velocity, which is 0 as the rocket starts from rest.
- a is the constant acceleration, which is 90.3 m/s² in this case.
- t is the time, which is 1.75 seconds.
Plugging the given values into the equation:
\[ h = 0 + (0 \cdot 1.75) + \frac{1}{2} \cdot (90.3) \cdot (1.75)^2 \]
Calculating further:
\[ h = 0 + 0 + \frac{1}{2} \cdot 90.3 \cdot (3.0625) \]
\[ h = 0 + 0 + 139.480 \]
Therefore, the maximum altitude reached by the rocket is approximately 139.480 meters above the ground.