A model rocket is launched straight upward with an initial speed of 51.3 m/s. It accelerates with a constant upward acceleration of 1.82 m/s2 until its engines stop at an altitude of 150 m. What is the maximum height reached by the rocket?
V^2 = Vo^2 + 2a*h
V^2 = 51.3^2 + 3.64*150 = 3177.69
V = 56.4 m/s.
hmax = (V^2-Vo^2)/2g
hmax = (0-56.4^2)/-19.6 = 162,3 m.
To find the maximum height reached by the rocket, we can use the kinematic equation of motion.
The equation we will use is:
vf^2 = vi^2 + 2ad
where,
vf is the final velocity (which is 0 m/s when the engines stop),
vi is the initial velocity (51.3 m/s),
a is the acceleration (1.82 m/s^2),
and d is the displacement (the maximum height reached, which we want to find).
Using the equation, we can rearrange it to solve for d:
d = (vf^2 - vi^2) / (2a)
Substituting the given values:
d = (0^2 - 51.3^2) / (2 * (-1.82))
Note: We have a negative acceleration because the rocket is decelerating as it moves upward.
Now, let's calculate the value of d:
d = (-2629.69) / (-3.64)
d ≈ 722.03 m
Therefore, the maximum height reached by the rocket is approximately 722.03 meters.