A NASA mission landed a mars rover onto Mars. The system (rover plus landing sys

Question

A NASA mission landed a mars rover onto Mars. The system (rover plus landing system) deployed its parachute at an altitude of 10.5 km over the landscape of Mars and a speed and mass of410 m/s and 3400 kg respectively. The parachute phase ends as the parachute separated from the rover at the end of the parachute phase at altitude 1700 m and a speed of 75 m/s. Thrusters on the rover begin to fire and exert an average upward force of 1.90*10^4 N for 39 seconds during the thruster phase. Gravity on mars is equal to 3.71 m/s^2 A) What was the total energy of the craft at the beginning of the parachute phase of the decent and at the end of that phase (beginning of thruster phase)? B) How much work did the parachute harness do on the rover? C)What was the average upward force applied by the parachute? D) What was the net vertical impulse of thrust + gravity experienced by the craft. during the thruster phase of the descent? E) What was the velocity of the rover at the end of the thrust phase of descent. just before touchdown? **Assume that there is no air drag on the rover itself - only on the parachute. Parachute and harness should be treated as external to the system being examined. Apply the energy principle

Explanation / Answer

initial energy E1 = m*g*h1 + 0.5*m*v1^2

E1 = (3400*3.71*10500)+(0.5*3400*410^2) = 418217000 J

final energy = E2 = m*g*h2 + 0.5*m*v262

E2 = (3400*3.71*1700)+(0.5*3400*75^2) = 31006300 J

B)

W = E1 - E2 = 387210700 J

(C)

W = F*dh

F = w/dh = -387210700/(10500-1700) = 44001.2 N

(D)

impulse = F*t = 1.9*10^4*39 = 741000 Ns

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