Question

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"`

Explanation:

`"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"`