A rocket is launched vertically from rest with a constant upward accceleration o

Question

A rocket is launched vertically from rest with a constant upward accceleration of 2.17 m/s2. Suddenly 29.6s after launch an unneeded fuel tank is jettisoned shooting it away from the rocket. A crew member riding in the rocket measures that the initial speed of the tank is 16.2 m/s and that it moves perpenicular to the rocket's path. The fuel tank feels no appreciable air resistance and feels only the force of gravity once it leaves the rocket. A) How fast is the rocket moving at the instant the fuel tank is jettisoned. B) What are the horizontal and verttical components of the fuel tank's velocity just as it is jettisoned as measured by a crew member in the rocket? C)What are the horizontal and vertical components of the fuel tank's velocity just as it is jettisoned as measured by a technician standing on the ground? D)At what angle with respect to the horizontal does the jettisoned fuel tank initially move, as measured by a crew member in the rocket? E)At what angle with respect to the horizontal does the jettisoned fuel tank initially move, as measured by a technician standing on the ground? F)What maximum height above the launch pad does the jettisoned tank reach?

Explanation / Answer

ar = 2.17 m/s2, ur =0, t = 29.6s, ut = 16.2 m/s

(A) Considering motion of the rocket in vertical up direction

vr = ur + art     ==> vr = 0 + 2.17 * 29.6

vr = 64.232 m/s

(B) Horizontal component = ut = 16.2 m/s

     Vertical component = 0

(C) Horizontal component = ut = 16.2 m/s

     Vertical component = -vr = -64.232 m/s

(D) 1 = tan-1(0/16.2) ==> 1 = 0o

(E) 2 = tan-1(-64.232/16.2) ==> 1 = -75.84o

(F) Using relation vt2 - ut2 = 2 (-g) h

0 - 16.22 = 2 (-9.8) h

h = 13.39 m

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