Like for the Mars Pathfinder mission, the entry and landing on Mars use a combin

Question

Like for the Mars Pathfinder mission, the entry and landing on Mars use a combination of aerodynamic drag (during entry, the spacecraft is protected by a heat shield), rockets, parachutes, and inflated airbags. The last phase of the entry & landing sequence is controlled by the on-board computer system. When the altitude reaches a certain critical value, the spacecraft velocity is 40 m/s. At this altitude, the airbags are inflated and a solid rocket engine is turned on to slow down the spacecraft prior to impact on the Martian soil. Knowing that the thrust generated by the rocket engine is 5150 N, and the propellant bums for 10 seconds before impact, what will be the velocity at impact in m/s. Assume that the spacecraft drag (due to parachute & inflated airbags) is constant and is 7500 N, and that the spacecraft mass is 1840 kg. Also, the Martian gravitational acceleration is equal to 3. 7 m/s^2. to solve this problem, make sure to include all forces acting on the spacecraft (weight, drag and thrust). Your Answer: Answer

Explanation / Answer

here,

Rocket thrust = 5150 N
Drag Force = 7500 N
g = 3.7 m/s^2
m = 1840 kg
u = 40 m/s
t = 10s

force acting to motion = Rocket thrust + Drag Force
Fr = 7500 + 5150
Fr = 12650 N

Force on Mars = M*g = 1840 * 3.7
Fm = 6808 N

Fnet = 12650 - 6808
Fnet = 5842 N

deacceleration due to net retarded force = Fnet/M
a = 5842/1850
a = 3.175 m/s^2

Therefore, From First Equation fo motion we have :
v = u - at
v = 40 - (3.175 * 10)
v = 8.25 m/s

The Velocity of Impact will be 8.25 m/s

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