A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 76.7 m/s2 for 1.89 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?
V1 = a*t = = 76.7 * 1.89 = 145 m/s.
h1 = 0.5a*t^2 = 0.5*76.7*1.89^2 = 137 m.
h2 = h1 + -V1^2/2g=137 + (-145)^2/-19.6 =
1210 m. Above gnd.
To find the maximum altitude reached by the rocket, we need to determine its final velocity after the given time of 1.89 seconds. Then we can use the kinematic equation to find the maximum height.
Step 1: Find the final velocity of the rocket.
We are given:
- Acceleration (a) = 76.7 m/s^2
- Time (t) = 1.89 seconds
- Initial velocity (u) = 0 m/s (since it starts from rest)
The final velocity (v) can be found using the formula:
v = u + at
Substituting the given values:
v = 0 + (76.7 m/s^2) * (1.89 seconds)
Step 2: Calculate the maximum height.
To find the maximum height, we can use the equation:
s = ut + (1/2)at^2
As the rocket starts from the ground, the initial displacement (s) is 0.
Substituting the values:
0 = (0 m/s) * (1.89 seconds) + (1/2) * (76.7 m/s^2) * (1.89 seconds)^2
Simplifying the equation, we can solve for the maximum altitude:
(1/2) * (76.7 m/s^2) * (1.89 seconds)^2 = s
s ≈ 137.1 meters
Therefore, the maximum altitude reached by the model rocket is approximately 137.1 meters above the ground.