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Answer :
The maximum height achieved by the rocket is approximately 1094.69 meters.
To find the maximum height the rocket will achieve, we will break the problem into two phases: the powered ascent and the free-fall descent.
Phase 1: Powered Ascent
First, we calculate the velocity of the rocket at the moment the motor stops using the formula:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (0 m/s, since it starts from rest)
- a is the acceleration (20 m/s²)
- t is the time (6 s)
Plugging in the values:
v = 0 m/s + (20 m/s² * 6 s) = 120 m/s
Phase 2: Free-Fall Descent
The rocket will continue to rise until its upward velocity decreases to 0 m/s due to gravity. For this phase, we use the following kinematic equation:
v² = u² + 2as
where:
- v is the final velocity (0 m/s)
- u is the initial velocity (120 m/s)
- a is the acceleration due to gravity (-9.8 m/s²)
- s is the displacement (height)
Plugging in the values:
0 = (120 m/s)² + 2(-9.8 m/s²)s
Solving for s:
0 = 14400 - 19.6s
19.6s = 14400
s = 14400 / 19.6 = 734.69 m
Total Height
The total height is the sum of the height covered during the powered ascent and the height during the free-fall phase:
Height during powered phase:
s = ut + 0.5at²
s = 0 * 6 + 0.5 * 20 m/s² * (6 s)² = 360 m
Total Height:
Total height = 360 m + 734.69 m = 1094.69 m
Hence, the maximum height the rocket will achieve is approximately 1094.69 meters.
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The maximum height is approximately 1094.69 meters.
To find the maximum height the rocket will achieve, we will break the problem into two phases: the powered ascent and the free-fall descent.
Phase 1: Powered Ascent
First, we calculate the velocity of the rocket at the moment the motor stops using the formula:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (0 m/s, since it starts from rest)
- a is the acceleration (20 m/s²)
- t is the time (6 s)
Plugging in the values:
v = 0 m/s + (20 m/s² × 6 s)
= 120 m/s
Phase 2: Free-Fall Descent
The rocket will continue to rise until its upward velocity decreases to 0 m/s due to gravity.
For this phase, we use the following kinematic equation:
v² = u² + 2as
where:
- v is the final velocity (0 m/s)
- u is the initial velocity (120 m/s)
- a is the acceleration due to gravity (-9.8 m/s²)
- s is the displacement (height)
Plugging in the values:
0 = (120 m/s)² + 2(-9.8 m/s²)s
Solving for s:
0 = 14400 - 19.6s
19.6s = 14400
s = 14400 / 19.6
= 734.69 m
Total Height
The total height is the sum of the height covered during the powered ascent and the height during the free-fall phase:
Height during powered phase:
s = ut + 0.5at²
s = 0 × 6 + 0.5 × 20 m/s² × (6 s)²
= 360 m
Total Height:
Total height = 360 m + 734.69 m
= 1094.69 m
