Question

5. Our heroic frog gets hungry and wanders away. She hops down the hall and into the elevator. as the elevator is accelerating upwards at α=2m/s/s she sees a tasty spider in its web at a height h = 85 cm above the floor of the elevator. (If the floor of the elevator moves, then the spider will move too.) This is the same frog, so it is capable of jumping with an initial velocity equal to the value you found in the previous problem (4.47 m/s)

Suppose that the frog jumps as high as she can to try to catch the spider, pushing off the ground with the same initial velocity as before.

draw a position vs time graph for the frog, the elevator, and the spider on the same set of axes

Answer 1

acceleration of elevator $\alpha$ = 2m/s/s

position of the elevator y_e(t) = 0.5$\alpha$t² = t²  

position of spider y_s(t) = h+0.5$\alpha$t² = 0.85 + t²

position of the frog y_f(t) = vt +0.5$\alpha$t² = 4.47t + t²