A rocket (stating from rest) travels upwards for 3 minutes at a constant acceleration of 16 m/s^2, and then coasts upwards until it reaches its maximum height. What it the rocket's maximum height?
how high does it go the first three min? What is it final velocity at the end of three min.
Then, from that height, start a free fall problem, given initial veloicty, how much higher will ti go.
Add the two heights.
I did this and found the answer to be 364,995.92 meters but I'm not sure that it is correct.
Anyone know if the answer I came up with is correct?
After 180 seconds it has risen
(1/2)*16*(180)^2 = 259,900 m and the velocity is 16*180 = 2880 m/s. The additional height that it rises while decelerating at rate -g for 2880/9.8 = 293.9 s is 423,184 s.
The sum of the two distances does not agree with your answer.
To find the rocket's maximum height, we can use the equations of motion. The rocket starts from rest, so its initial velocity (u) is 0 m/s. It travels upwards for 3 minutes, which is equivalent to 3 × 60 = 180 seconds. The acceleration (a) is given as 16 m/s². We need to find the maximum height (h).
We can use the equation of motion, which relates displacement (s), initial velocity (u), acceleration (a), and time (t):
s = ut + 0.5at²
Since the rocket starts from rest, the equation simplifies to:
s = 0 × t + 0.5at²
s = 0.5at²
For the first 3 minutes, we can use this equation to find the displacement:
s1 = 0.5 × 16 × (3 × 60)²
s1 = 0.5 × 16 × 180²
s1 = 0.5 × 16 × 32400
s1 = 259200 m
Therefore, the displacement during the upward acceleration phase is 259200 meters.
Next, the rocket coasts upwards until it reaches its maximum height. During this phase, the rocket's acceleration is 0 m/s², and its initial velocity is the final velocity attained during the upward acceleration phase.
We can use the equation v = u + at to find the final velocity (v) attained during the upward acceleration phase. Since the acceleration is constant (16 m/s²) and the initial velocity (u) is 0 m/s, the equation simplifies to:
v = 16 × (3 × 60)
v = 16 × 180
v = 2880 m/s
Now, using the equation v² = u² + 2as, we can find the maximum height (h):
0 = (2880)² + 2 × a × h
0 = 8294400 + 0 × h
h = -8294400 / 0
Since the denominator is 0, the height seems to be undefined. This suggests that the rocket does not reach a maximum height after the coasting phase, and may continue to accelerate indefinitely or reach outer space.
Therefore, based on the given information, we cannot determine the rocket's maximum height.