A rubber ball is tossed straight up from a height of 10 feetwith a velocity of 78 feet per second. The first time it hits theground (y = 0), it rebounds with a velocity of 64 feet per second2. The second time it hits the floor, it rebounds with a velocity of48 feet per second. Before the first bounce 1. Find the function y= h1(t) for the height of the ball before its first bounce. 2. Findthe time t1 when the ball hits the ground for the first time. Thefunction h1(t) then describes the height of the ball over the timeinterval [0, t1] before the ball’s first bounce. 3. Find thevelocity v1(t) of the ball over the interval [0, t1]. 4. Determinethe time t when the ball reaches its first peak height. What is theheight of the ball at this time? Between the first and secondbounce 5. Find the function y = h2(t) for the height of the ballbetween the first and second bounce. 6. Find the time t2 when theball hits the ground for the second time. The function h2(t) thendescribes the height of the ball over the time interval [t1, t2].7. Find the velocity v2(t) of the ball over the interval [t1, t2].8. Determine the time t when the ball reaches its second peakheight. What is the height of the ball at this time? Between thesecond and third bounce 9. Find the function y = h3(t) for theheight of the ball between the second and third bounce. 10. Findthe time t3 when the ball hits the ground for the third time. Thefunction h3(t) then describes the height of the ball over the timeinterval [t2, t3]. 11. Find the velocity v3(t) of the ball over theinterval [t2, t3]. 12. Determine the time t when the ball reachesits third peak height. What is the height of the ball at this time?Graphs 13. On the coordinate systems below sketch accurate graphsof the height and velocity of the ball over the time interval [0,t3].
