Bob has just finished climbing a sheer cliff above a level beach and wants to figure out how high he climbed. All he has to use is baseball, a stopwatch, and friend on the ground below with a long measuring tape. Bob is a pitcher and knows that the fastest he can throw the ball is about v_0= 34 m/s. Bob starts the stopwatch as he throws the ball, with no way to measure the ball’s initial trajectory, and he watches carefully. The ball rises and then falls, and after t_1= 0.510 s the ball is once again level with Bob. Bob cannot see we’ll enough to time when the ball hits the ground. Bob’s friend the measures that the ball hit the ground x= 127 m from the base of the cliff. How high above the beach was the ball when it was thrown? A projectile is launched from ground level with an initial speed of 45.5 m/s at an angle of 32.3 degrees above the horizontal. It strikes a target in the air 1.83 s later. What is the horizontal distance from where the projectile was launched to where it hits…

A tourist at a rim of a canyon yells "hello!" toward the opposite side. She hears the echo "hello" four seconds later. If the speed of sound is 340 m/s, how far away was the canyon wall that produced the echo?

In tennis, one of the primary ways to win a point is by making the ball bounce twice on your opponent's side of the court. A tennis player hits a ball at a velocity of 50 m/s at a 0 degree angle from 1m high. When the ball bounces it reflects its velocity angle perfectly and loses 30% of its speed. How long does the other player have to return the ball before the second bounce?