(Solved): A diver leaps from a 3 meter springboard. His feet leave the board at time \( t=0 \), he reaches hi ...

A diver leaps from a 3 meter springboard. His feet leave the board at time \( t=0 \), he reaches his maximum height of \( 4.5 \mathrm{~m} \) at \( t=1 \) seconds, and enters the water at \( t=2.73 \). Once in the water, the diver coasts to the bottom of the pool (depth \( 3.5 \mathrm{~m}) \), touches bottom at \( t=4.73 \) ( 2 seconds later), rests for one second, and then pushes off the bottom. From there he coasts to the surface, and takes his first breath at \( t=6.73 \). Let \( s(t) \) denote the function that gives the height of the diver's feet (in meters) above the water at time \( t \). (Note that the "height" of the bottom of the pool is \( -3.5 \) meters.) Sketch a carefully labeled graph of \( s(t) \) on the provided axes below as well as a second graph for the velocity.