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Consider a rocket which has a mass of 2.10 x 106 kg at takeoff, and its engines produce a constant thrust of 3.1 x 107 N as it takes off vertically. Choose the best response for the three quantities below:a) the initial acceleration of the rocket;b) the time needed for the rocket to reach a speed of 50 m/s, assuming constant mass and thrust; andc) description of the actual acceleration and time needed to reach 50 m/s factoring in that as the rocket ascends, fuel is expelled and thus the mass decreases significantly.Group of answer choicesa) 𝑎𝑜=4.96𝑚/𝑠2b) 𝑡=10.1𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will not change, so the net force acting on the rocket will be constant. So, the acceleration will remain constant as the rocket burns fuel and the time it would take to reach 50 m/s will still be about 10.1 seconds.a) 𝑎𝑜=4.96𝑚/𝑠2b) 𝑡=10.1𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will become lessened due to the loss of mass and so the net force acting upward will become larger. So, the acceleration will will increase as the rocket burns fuel and the time it would take to reach 50 m/s will be less than 10.1 secondsa) 𝑎𝑜=14.8𝑚/𝑠2b) 𝑡=3.38𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will not change, so the net force acting on the rocket will be constant. So, the acceleration will remain constant as the rocket burns fuel and the time it would take to reach 50 m/s will still be about 3.38 secondsa) 𝑎𝑜=14.8𝑚/𝑠2b) 𝑡=3.38𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will become lessened due to the loss of mass and so the net force acting upward will become larger. So, the acceleration will will increase as the rocket burns fuel and the time it would take to reach 50 m/s will be less than 3.38 seconds

Question

Consider a rocket which has a mass of 2.10 x 106 kg at takeoff, and its engines produce a constant thrust of 3.1 x 107 N as it takes off vertically. Choose the best response for the three quantities below:a) the initial acceleration of the rocket;b) the time needed for the rocket to reach a speed of 50 m/s, assuming constant mass and thrust; andc) description of the actual acceleration and time needed to reach 50 m/s factoring in that as the rocket ascends, fuel is expelled and thus the mass decreases significantly.Group of answer choicesa) 𝑎𝑜=4.96𝑚/𝑠2b) 𝑡=10.1𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will not change, so the net force acting on the rocket will be constant. So, the acceleration will remain constant as the rocket burns fuel and the time it would take to reach 50 m/s will still be about 10.1 seconds.a) 𝑎𝑜=4.96𝑚/𝑠2b) 𝑡=10.1𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will become lessened due to the loss of mass and so the net force acting upward will become larger. So, the acceleration will will increase as the rocket burns fuel and the time it would take to reach 50 m/s will be less than 10.1 secondsa) 𝑎𝑜=14.8𝑚/𝑠2b) 𝑡=3.38𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will not change, so the net force acting on the rocket will be constant. So, the acceleration will remain constant as the rocket burns fuel and the time it would take to reach 50 m/s will still be about 3.38 secondsa) 𝑎𝑜=14.8𝑚/𝑠2b) 𝑡=3.38𝑠c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will become lessened due to the loss of mass and so the net force acting upward will become larger. So, the acceleration will will increase as the rocket burns fuel and the time it would take to reach 50 m/s will be less than 3.38 seconds

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Solution

The correct answer is:

a) 𝑎𝑜=14.8𝑚/𝑠2 b) 𝑡=3.38𝑠 c) Assuming the rocket can produce a constant thrust force, F0, the gravitational force acting downward on the rocket will become lessened due to the loss of mass and so the net force acting upward will become larger. So, the acceleration will increase as the rocket burns fuel and the time it would take to reach 50 m/s will be less than 3.38 seconds.

Here's why:

a) The initial acceleration of the rocket can be calculated using Newton's second law, F=ma. The force (F) is the thrust produced by the engines, and the mass (m) is the mass of the rocket at takeoff. So, 𝑎𝑜 = F/m = (3.1 x 107 N) / (2.10 x 106 kg) = 14.8 m/s2.

b) The time needed for the rocket to reach a speed of 50 m/s can be calculated using the equation of motion, v = at. Rearranging for time, t = v/a = 50 m/s / 14.8 m/s2 = 3.38 s.

c) As the rocket ascends and burns fuel, its mass decreases. This means the gravitational force acting on it also decreases, so the net force acting on the rocket (which is the difference between the thrust force and the gravitational force) increases. This results in an increase in acceleration. Therefore, the time it would take to reach 50 m/s would be less than the time calculated assuming constant mass and thrust.

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