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A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from the earth's surface would be
- a)245 m
- b)490 m
- c)980 m
- d)735 m
Correct answer is option 'D'. Can you explain this answer?
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Given: Acceleration of rocket = 19.6 m/sec2, Time taken to switch off engine = 5 sec
To find: Maximum height of rocket from the earth's surface
We can use the kinematic equation:
v^2 = u^2 + 2as
where, v = final velocity (when engine is switched off), u = initial velocity (when rocket is fired), a = acceleration, s = distance travelled
Initial velocity, u = 0 (since the rocket was fired from rest)
Final velocity, v = u + at = 0 + 19.6 x 5 = 98 m/sec
Distance travelled, s = ut + 1/2at^2 = 0 x 5 + 1/2 x 19.6 x 5^2 = 245 m
Now, we can use the formula for maximum height reached by the rocket:
h = s + u^2/2g
where, g = acceleration due to gravity = 9.8 m/sec2
Substituting the values, we get:
h = 245 + 0^2/2 x 9.8 = 245 + 0 = 245 m
Therefore, the maximum height of the rocket from the earth's surface is 245 m.
To find: Maximum height of rocket from the earth's surface
We can use the kinematic equation:
v^2 = u^2 + 2as
where, v = final velocity (when engine is switched off), u = initial velocity (when rocket is fired), a = acceleration, s = distance travelled
Initial velocity, u = 0 (since the rocket was fired from rest)
Final velocity, v = u + at = 0 + 19.6 x 5 = 98 m/sec
Distance travelled, s = ut + 1/2at^2 = 0 x 5 + 1/2 x 19.6 x 5^2 = 245 m
Now, we can use the formula for maximum height reached by the rocket:
h = s + u^2/2g
where, g = acceleration due to gravity = 9.8 m/sec2
Substituting the values, we get:
h = 245 + 0^2/2 x 9.8 = 245 + 0 = 245 m
Therefore, the maximum height of the rocket from the earth's surface is 245 m.
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A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from the earth's surface would bea)245 mb)490 mc)980 md)735 mCorrect answer is option 'D'. Can you explain this answer?
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