Answer to Question #169145 in Physics for Rijak

Question #169145

A lunar lander is descending toward the moon’s surface. Until the lander reaches the

surface, its height above the surface of the moon is given by 𝑦(𝑑) = 800 π‘š βˆ’ (60.0 π‘š/𝑠) 𝑑 + (1.05 π‘š/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?


1
Expert's answer
2021-03-08T08:27:21-0500

(a) Velocity is the derivative of position with respect to time:


vy=dydt,v_y=\dfrac{dy}{dt},vy=ddt(800βˆ’60t+1.05t2)=βˆ’60+2.1t.v_y=\dfrac{d}{dt}(800-60t+1.05t^2)=-60+2.1t.

Finally, we can find the initial velocity of the lander, at t=0t=0 :


vy0=βˆ’60+2.1β‹…0=βˆ’60 ms.v_{y0}=-60+2.1\cdot0=-60\ \dfrac{m}{s}.

(b) The lunar lander reaches the lunar surface when y(t)=0y(t)=0:


1.05t2βˆ’60t+800=01.05t^2-60t+800=0

This quadratic equation has two roots: t1=35.9 st_1=35.9\ s and t2=21.2 s.t_2=21.2\ s. The correct answer is t=21.2 st=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:


vy=βˆ’60 ms+2.1 ms2β‹…21.2 s=βˆ’15.5 ms.v_y=-60\ \dfrac{m}{s}+2.1\ \dfrac{m}{s^2}\cdot21.2\ s=-15.5\ \dfrac{m}{s}.

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