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 "t=0" :
(b) The lunar lander reaches the lunar surface when "y(t)=0":
This quadratic equation has two roots: "t_1=35.9\\ s" and "t_2=21.2\\ s." The correct answer is "t=21.2\\ s" (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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