A small 7.70-kg rocket burns fuel that exerts a time-varying upward force on the

Question

A small 7.70-kg rocket burns fuel that exerts a time-varying upward force on the rocket. This force obeys the equation F=A+Bt2. Measurements show that at t=0, the force is 114.0 N , and at the end of the first 1.70 s , it is 190.0 N .

Find the constant A.

Find the constants B.

Find the net force on this rocket the instant after the fuel ignites.

Find the acceleration of this rocket the instant after the fuel ignites.

Find the net force on this rocket 3.30 safter fuel ignition.

Find the acceleration of this rocket 3.30 s after fuel ignition.

Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.30 s after fuel ignition?

Explanation / Answer

Upward force F = A + Bt2

1] at t = 0s, F = A + B(0) = A

therefore, A = 114 N

2] and at t = 1.7s;

190 = 114 + B(1.7)2

=> B = 26.297 kgm

3] The net force at t = 0s [after the fuel starts to ignite] will be:

Fnet = 114 - mg = 114 - 7.7(9.8) = 38.54 N

4] Fnet = ma

=> 38.54 = 7.7a

=> a = 5.00 m/s2

this is the acceleration of the rocket the instant the fuel starts to ignite.

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