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Problem: After parachuting through the Martian atmosphere, the Mars Science Laboratory executed a complex series of maneuvers that successfully placed the rover Curiosity on the surface of Mars in 2012. The final 22 s of the landing involved, in this order, firing rockets (1) to maintain a constant downward velocity of 32 m/s, (2) to achieve a constant deceleration that brought the downward speed to 0.75 m/s, and (3) to hold that constant velocity while the rover was lowered on cables from the rest of the spacecraft. The rover's touchdown was indicated by a sudden decrease in the rocket thrust needed to maintain a constant velocity. (Figure 1) shows the rocket thrust (upward force) as a function of time during this final 22 s of the flight and the first few seconds after touchdown. Remember that all this happened on Mars, so gravity is different.* surface gravity on Mars is approx. 3.71 m/s^2(a) Find the magnitude of the spacecraft's acceleration during the constant-deceleration phase.(b) Determine the mass of the so-called powered descent vehicle, meaning the spacecraft with the rover attached.(c) Determine the mass of the rover alone.

FREE Expert Solution

In this problem, we have a narration where we are supposed to deduce meaningful information. 

From Newton's second law, the force must be constant to maintain a constant acceleration. Thus, the phases of constant acceleration are marked by the horizontal parts of the graph. 

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Problem Details

After parachuting through the Martian atmosphere, the Mars Science Laboratory executed a complex series of maneuvers that successfully placed the rover Curiosity on the surface of Mars in 2012. The final 22 s of the landing involved, in this order, firing rockets (1) to maintain a constant downward velocity of 32 m/s, (2) to achieve a constant deceleration that brought the downward speed to 0.75 m/s, and (3) to hold that constant velocity while the rover was lowered on cables from the rest of the spacecraft. The rover's touchdown was indicated by a sudden decrease in the rocket thrust needed to maintain a constant velocity. (Figure 1) shows the rocket thrust (upward force) as a function of time during this final 22 s of the flight and the first few seconds after touchdown. Remember that all this happened on Mars, so gravity is different.

* surface gravity on Mars is approx. 3.71 m/s^2

(a) Find the magnitude of the spacecraft's acceleration during the constant-deceleration phase.

(b) Determine the mass of the so-called powered descent vehicle, meaning the spacecraft with the rover attached.

(c) Determine the mass of the rover alone.

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