A model rocket is launched straight upward with an initial speed of 47.7 m/s. It accelerates with a constant upward acceleration of 2.02 m/s2 until its engines stop at an altitude of 157 m. What is the maximum height reached by the rocket?
find the speed at engine shutdown, and the height of it at that time.
H=157 m given
vf^2=2ah solve for vf, a, h given.
knowing vf at shutdown, what is the height it now goes?
speed at the top is zero, so
0=Vfabove^2 + 2ah where a is now -9.8m/s^2, solve for h
final height: h+157
To find the maximum height reached by the rocket, we can use the equations of motion. The initial velocity (u) of the rocket is 47.7 m/s and the final velocity (v) is 0 m/s (since the engines stop). The acceleration (a) is given as 2.02 m/s². We need to find the maximum height (h) reached by the rocket.
We can use the equation of motion: v² = u² + 2a(h - s), where s is the initial displacement (0 m). Rearranging the equation, we get:
v² - u² = 2a(h - s)
Substituting the values into the equation:
0² - (47.7 m/s)² = 2(2.02 m/s²)(h - 0)
-47.7² = 4.04h
h = (-47.7²) / (4.04)
Calculating this, we get:
h ≈ - 566.62 m
The negative value is not physically meaningful in this context, so we can discard it. Thus, the maximum height reached by the rocket is approximately 566.62 meters.