A model rocket is launched straight upward with an install speed of 57.6 m/s. it accelerates with a constant upward acceleration of 1.70m/s^2 until its engines stop at an altitude of 240m.
A. What is the maximum height reached by the rocket? The acceleration of gravity is 9.81m/s^2
B. When does the rocket reach its maximum height?
C. How long is the rocket in the air?
http://www.jiskha.com/display.cgi?id=1378928235
lfjh
To find the answers to these questions, we can use the equations of motion for uniformly accelerated motion. These equations are:
1. v = u + at
2. s = ut + (1/2)at^2
3. v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement
Now let's solve the questions step by step:
A. What is the maximum height reached by the rocket?
First, we need to find the time it takes for the rocket to reach its maximum height. The final velocity at the maximum height is zero because the rocket stops momentarily. So we can use Equation 1 to find this time:
0 = 57.6 + (-1.70)t
1.70t = 57.6
t = 57.6 / 1.70
t ≈ 33.9 seconds
Now we can use Equation 2 to find the maximum height:
s = (57.6)(33.9) + (1/2)(-1.70)(33.9)^2
s ≈ 1938.8 - 2013.73
s ≈ -74.93 meters
The maximum height reached by the rocket is 74.93 meters above the launch point.
B. When does the rocket reach its maximum height?
From our previous calculation, we found that the time it takes for the rocket to reach its maximum height is approximately 33.9 seconds.
C. How long is the rocket in the air?
To calculate the total time the rocket is in the air, we need to find the time it takes to reach the maximum height and double it because the rocket will take the same amount of time to come back down. So the total time is:
Total time = 2 * 33.9
Total time ≈ 67.8 seconds
Therefore, the rocket is in the air for approximately 67.8 seconds.