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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.

What scientific concept do you need to know in order to solve this problem?

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