If a rocket with a mass of 4000 tons vertically accelerates at a rate of # 4/7 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 4 seconds?

Answer 1

#"Power " = 4.3 xx 10^7" Watts"#

#"Power" = "Energy" -: "Time"#

#"Energy" = "Potential Energy" + "Kinetic Energy"#

#"Potential Energy" = mgh#

where the mass, #m = 3628739" kg (4000 tons)"#, the gravitational acceleration, #g = 9.8" m"/"s"^2#, and the height, #h = 1/2(4/7" m"/"s"^2)(4" s")^2#

#"Potential Energy" = (3628739" kg")(9.8" m"/"s"^2)(1/2)(4/7" m"/"s"^2)(4" s")^2#

#"Kinetic Energy " = 1/2mV^2 = 1/2m(at)^2 = (3628739" kg")(1/2){(4/7" m"/"s"^2)(4" s")}^2#

Because both terms contain #t^2# and we are about to divide by t, we will write everything with one less power to t and be done with it.

#"Power " = (1/2)(3628739" kg")(4" s"){(9.8" m"/"s"^2)(4/7" m"/"s"^2) + (4/7" m"/"s"^2)^2}#

#"Power " = 4.3 xx 10^7" Watts"#

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Answer 2

Elena Albarran

The power exerted by the rocket to maintain its acceleration at 4 seconds is 10,285.714 kW.

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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.