Pirates are attacking the Caribbean island of Nevis Soldiers

Pirates are attacking the Caribbean island of Nevis! Soldiers manning a coastal fortress rush to their cannons and prepare to defend the port by sinking the pirate ship George and Edward are manning a cannon that sits fifty feet above the water in a fortress tower. They load, aim and fire their cannon. The cannon ball has an initial vertical velocity of 72 feet per second and hits the pirate ship ten feet above the water line exactly 5.0 seconds later. Complete the following tasks: Create a quadratic function describing the height of the cannonball above the water with respect to time t. After how many seconds will the cannonball reach its maximum height? Round your answer to the nearest hundredth of a second. Find the maximum height of the cannonball in feet. The pirates are still approaching! George and Edward fire a second shot that hits the pirate ship only one foot above the water line, finally sinking it. For this shot, the cannonball reaches its target after only 3.5 seconds. What was the initial vertical velocity of their second cannonball in feet per second?

Solution

22.

vertical vel. of the ball = 72 ft /s.

vertical position of the ball

y(t) = 50 +72t -32t²/2 (we take g = 32 ft/s/s)

   = 50+72t-16t²

Y is maximum when dy/dt =0

72-32t = 0 , t = 2.25 s

maximum height

y(t=2.25) = 50+72*2.25 -16*2.25² = 134.56

25.

Let v be the initial vertical velocity

then     y(t) = 50+vt-16t²

the ball hits the ship after t=3.5 s and y=1 ft above the water

1 = 50+ v*3.5 -16*3.5²

      v =     42 ft/s