A rocket is launched vertically from rest with a constant upward acceleration of

Question

A rocket is launched vertically from rest with a constant upward acceleration of 2.82 m/s2 . Suddenly 16.9 s after launch, an unneeded fuel tank is jettisoned by shooting it away from the rocket. A crew member riding in the rocket measures that the initial speed of the tank is 19.1 m/s and that it moves perpendicular 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) 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?

Enter your answers numerically separated by a comma.

B) At what angle with respect to the horizontal does the jettisoned fuel tank initially move, as measured by a crew member in the rocket?

C) At what angle with respect to the horizontal does the jettisoned fuel tank initially move, as measured by a technician standing on the ground?

D) What maximum height above the launch pad does the jettisoned tank reach?

Explanation / Answer

A)

Velocity of the tank with respect to the rocket, Vtr = 19.1 i <------- i = unit vector in the direction to x axis

Velocity of the the rocket with repect to ground , Vrg = 2.83*16.9 j = 47.8 j

So, velocity of the tank with repect to ground , Vtg = Vtr + Vrg = 19.1 i + 47.8 j

So, horizontal component = 19.1 m/s

vertical component = 47.8 m/s

B)

angle = 90 deg <---- given in the question itself

C)

angle = atan(47.8/19.1) = 68.2 deg

D)

maximum height , h = 47.8^2/(2*9.8) = 116.6 m

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