A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 75.5 m/s2 for 1.58 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?
the rocket attains a velocity of
75.5 * 1.58 or 119.3 m/s
since it started from zero, the average velocity for the 1st part of the flight is 119.3/2 or 59.65 m/s
it runs out of fuel at a height of
1.58 * 59.65 or 94.24 m
in the 2nd part of the flight, the rocket is decelerated by gravity for
119.3 / 9.8 or 12.17 s
since the rocket is slowing back to zero (at max height), the average velocity is the same as during the 1st part of the flight
the height from fuel exhaustion to peak is 59.65 * 12.17 or 725.94 m
the max altitude is
94.24 m + 725.94 m or 820. m
Why did the model rocket join a support group? Because it felt like it was losing altitude in life!
To find the maximum altitude reached by the rocket, we can use the kinematic equation:
h = v0t + (1/2)at^2
Where:
h = height (maximum altitude)
v0 = initial velocity (0 m/s, since the rocket starts from rest)
t = time (1.58 seconds)
a = acceleration (75.5 m/s^2)
Plugging in the values, we get:
h = (0)(1.58) + (1/2)(75.5)(1.58)^2
Simplifying this equation, we have:
h = (1/2)(75.5)(2.4964)
Calculating the equation, the maximum altitude reached by the rocket is:
h ≈ 94.6 meters
So, the rocket will reach a maximum altitude of approximately 94.6 meters above the ground. Just remember to keep your expectations as high as this rocket's altitude!
To find the maximum altitude reached by the rocket, we can use the equations of motion.
Step 1: Determine the initial velocity.
Since the rocket starts from rest, the initial velocity (v₀) is 0 m/s.
Step 2: Calculate the time taken to reach maximum altitude.
The rocket's acceleration is given as 75.5 m/s², and the time taken is 1.58 seconds.
Step 3: Find the final velocity at maximum altitude.
We can use the equation:
v = v₀ + at
Substituting the known values:
v = 0 + 75.5 × 1.58
Simplifying:
v = 119.39 m/s
Step 4: Calculate the maximum altitude.
To find the maximum altitude, we can use the equation:
Δh = v₀t + (1/2)at²
Substituting the known values:
Δh = (0 × 1.58) + (1/2) × 75.5 × (1.58)²
Simplifying:
Δh = 119.39 - (1/2) × 75.5 × (2.4964)
Simplifying further:
Δh = 119.39 - 94.24482
Final calculation:
Δh = 25.14518 m
Therefore, the maximum altitude reached by the rocket is approximately 25.15 meters above the ground.
To find the maximum altitude reached by the rocket, we need to use the equations of motion. In this case, we can use the kinematic equation for displacement:
s = ut + 0.5at^2
where:
s = displacement (maximum altitude)
u = initial velocity (0 m/s, as the rocket starts from rest)
a = constant acceleration (75.5 m/s^2)
t = time (1.58 seconds)
Plugging in the values, we get:
s = (0) + 0.5 * (75.5) * (1.58^2)
s = 0 + 0.5 * 75.5 * 2.4964
s = 0 + 94.530
Therefore, the maximum altitude reached by the rocket is approximately 94.530 meters above the ground.