Question

Problem Report 2a: The Diving Problem (e) Find the average velocity of the diver for each of the following time intervals Problem Report 2a: The Diving Problem A diver leaps from a 3 meter springboand. His feet leave the board at time 0 seconds, he reaches his maximum height of 5 meters at 1 second, and enters the water at 3 seconds. Once in the water, the diver coasts to the bottom of the pool (depth & meters), toaches bottom at 7 seconds, rests for one second, and then pushes off the bettom From there he coasts to the surtace, and takes his Erst breath at 13 seconds (showing your work and labeling each answer with appropriate unis) AND state whether the diver is speeding up, slowing down, or staying at a constant rate during each time isterval: L o,1)seconds ii tE (1.3)seconds ii. t E (3,7)seconds (a) Let s() denote the function that gives the height of the diver's feet (in meters) above the water at time & (Note that the "height" of the bottom of the peol is-4 meters.) Sketch an accurate graph of s(t) on the provided axes in Figure 1.1.5 at the right using the information given above Remember to think abost the diver's movenents as you connect the points (using carvature of the graph appropriately). Also add the unit labels to both the horizontal and vertical axes. 10 1 6 (78)secemds v t(R,13)seconds (f) Let the function吖 represent the Figure 1.1.5. Axes for plotting it) in part (a instantaneous vertical velocity of the diver at time r(le, the speed at which the height fanction s(t) is changing). Based on your understanding of the diver's behavior from your work for parts (a) through (e) above sketch a graph of vt) on the axes provided in Figure 1.1.6 at the right as accurately as possible. [Hist: Use the average velocities and think ahout whether the diver is speeding up or slowing down as you connect the points where you do know the instantaneous velocity, using curvature of the graph appropniatelyl Also add the ueit (b) When is the velocity of the diver zero and why? (Include all times whes velocity is era.) 2 46 8 10 12 ) When is the velocity of the diver positive and what does this mean the diver is Figure 1.1.6. Axes for plotting elt) in part (c) doing? (laclude all times when velocity is positive.) axes (2) Compare your graphs of s(t) from part (a) with v) from part () and answer the following questions. (Hint: Your two graphs should NOT be the same] i. What can you say is always true about the velocity graph when the heigh ) When is the velocity of the diver negative and what does this mean the diver is function is increasing doing? (leclude all times when velocity is negative.) i What can you say is always true abost the velocity graph when the heipht function is decreasing? Page 2 of Page 1 of 2

Answer 1