The magnitude of the acceleration that the engine must produce is 0.065 m/s².
What is acceleration?
Acceleration is given by the ratio of Resultant or total force acting on any object and the its mass.
It can also be defined as the rate change of velocity with time.
acceleration a = (Δv) / (Δt)
Given is a lunar probe is moving 1670 m/s at a 73° angle. it needs to land on the moon 3.71 x 10⁸ m away in a 46° direction in 8.64 x 10⁴ s.
The initial velocity will be
1670 x cos (73°-46°) = 1487.981 m/s
Using the second equation of motion, we have
s = ut + 1/2 at²
The final velocity will be zero after landing on Moon.
Substituting the values, we have
3.71 x 10⁸= 1487.981 x 8.64 x 10⁴ + 1/2 a ( 8.64 x 10⁴)²
Solving the equation, we get
acceleration, a = 0.065 m/s²
Thus, the magnitude of the acceleration that the engine must produce is 0.065 m/s²
Learn more about acceleration.
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