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The Daredevil A daredevil triesjuniping off the roofofa building with a loose billowing cape ofeloth, hoping the cloth will slow him down. He jumps from an unknown hcight, yo. and lands at y = 0 two seconds later, While he is falling his velocity in m/s is given by the function: v(t) = 9,8t + 2:2 Note that here it is assumed he jumps at t = 0 and that up is the positive direction. The presence oi'the 22:2 term represents the action of the cape to slow him down. 1. What is the acceleration as a function of time that he experiences while in the air? a(t) = 2. What is his position as a function of time? Use the integral. Also use the fact that he is in the air for exactly 2 seconds and lands at y = 0 to determine the unknown constant of integration, C. ytr): _ 3. From what height did he jump, and what was his nal velocity with which he hit the ground? Height = v = 4. Also, from what height could he havejumped without his cape to strike the ground with the same speed? without cape, Height = Let's Play Ball! A 0.5 kg baseball is throvm at a speed of 13 m/s. You hit it with the bat, and it goes straight back to the pitcher. This means the collision is one dimensional, along the line between you and the pitcher. The force of collision last for 0.04 seconds and is given by the function: F(t) = 590 sin(251rt) N for 0