A rocket with mass M is fired from rest from the ground at an angle of . The exh

Question

A rocket with mass M is fired from rest from the ground at an angle of . The exhaust exerts a force of constant magnitude F at that same angle for a time interval of t and then cuts out. Ignore the mass of the fuel consumed and neglect drag forces

(a) What is the altitude of the rocket when the exhaust cuts out? Express your answer in terms of the following variables: M, , F, t, and/or g.

(b) Calculate the numerical answer for part (a) using the following values: M = 3050 kg, = 63, F = 63.5 kN, and t = 43.0s

Explanation / Answer

a)

let the force acting is F

Using second law of motion

m * a = F - m * g

a = (F * sin()/m - g)

using second equation of motion

h = 0.5 *a * t^2

h = 0.5 * (F*sin()/m - g)^2 * t^2

the altitude of rocket when the exhaust cuts out is 0.5 * (F*sin()/m - g)^2 * t^2

b)

Putting values in equation

h = 0.5 * (F*sin()/m - g)^2 * t^2

h = 0.5 * (63.5 *10^3 * sin(63)/3050 - 9.8) * 43^2

h = 8090 m

the altitude of the rocket when the exhaust cuts out is 8090 m

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