If a rocket with a mass of #3500 "tons"# vertically accelerates at a rate of # 8/5 "m/s"^2#, how much power will the rocket have to exert to maintain its acceleration at 12 seconds?

Answer 1

The power is #=766.1MW#

The mass of the rocket is #m=3500 000kg#
The acceleration is #a=8/5ms^-2#
The acceleration due to gravity is #=9.8ms^-2#

According to Newton's second Law, the net force on the rocket is

#F=m(a+g)=3500000*(9.8+1.6)=39900000N#
Assuming that the initial velocity of the rocket is #u=0ms^-1#
The velocity after #t=12s# is
#v=u+at=0+12*8/5=19.2ms^-1#

The power is

#P=Fv=39900000*19.2=766100000W=766100kW=766.1MW#
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Answer 2

To find the power exerted by the rocket, you can use the equation: Power = Force × Velocity. First, calculate the force using Newton's second law: Force = mass × acceleration. Then, use the formula for power and substitute the calculated force and the given velocity (since velocity is the rate of change of displacement and is constant during vertical acceleration).

Given: Mass (m) = 3500 tons Acceleration (a) = 8/5 m/s^2 Time (t) = 12 seconds

Calculations: Force = mass × acceleration Force = 3500 tons × (8/5 m/s^2)

Convert tons to kilograms: 1 ton = 1000 kg Mass = 3500 tons × 1000 kg/ton Mass = 3,500,000 kg

Force = 3,500,000 kg × (8/5 m/s^2)

Force = 5,600,000 N

Power = Force × Velocity Power = 5,600,000 N × (8/5 m/s)

Power = 8,960,000 watts

Therefore, the rocket will have to exert approximately 8,960,000 watts of power to maintain its acceleration after 12 seconds.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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