Joan is looking straight out a window of an apartment building at a height of 32

Question

Joan is looking straight out a window of an apartment building at a height of 32 ft from the ground. A boy on the ground throws a tennis ball straight up by the side of the building where the window is located. Suppose the height of the ball (measured in feet) from the ground at time t is h(t)= 4 + 64t -16t^2 A. show that h(0)=4 and h(2)=68 b. use the intermediate value theorem to conclude that the ball must cross joan's line of sight at least once. c. at what time(s) does the ball cross joan's line of sight? interpret your results. c.

Explanation / Answer

h(0) = 4 +64(0) -16(0) =4 h(2) =4 + 64(2) -16(4) =4+128-64 =68 now at t=0 h=4 and at t=2 h=68 so there must have been t where h=32 as h(t) is continuos so there exist atleast one t between (0,2) such that h=32 Let that time be t now h(t)=4+64t-16t^2 =32 solving this equations gives two real roots t=0.5 and t=3.5 thus ball is at h=32 twice .

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