A lunar lander is descending toward the moonβs surface. Until the lander reaches the
surface, its height above the surface of the moon is given by π¦(π‘) = 800 π β (60.0 π/π ) π‘ + (1.05 π/s2) t2 .
(a) What is the initial velocity of the lander, at t=0?
(b) What is the velocity of thel landerjust before it reaches the lunar surface?
(a) Velocity is the derivative of position with respect to time:
Finally, we can find the initial velocity of the lander, at :
(b) The lunar lander reaches the lunar surface when :
This quadratic equation has two roots: and The correct answer is (we choose the least time to land to the lunar surface).
Finally, we can find the velocity of the lander just before it reaches the lunar surface:
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