The Roadrunner is standing at the edge of a cliff 800 meters above the ground. Wile E. Coyote is 42 meters above the ground on a ledge directly below...

The Roadrunner is standing at the edge of a cliff 800 meters above the ground. Wile E. Coyote is 42 meters above the ground on a ledge directly below the Roadrunner. Wile E. has purchased a spring catapult from Acme Catapult Company. This catapult will propel Wile E. upward with an initial velocity of 117 meters per second. The equation that gives the height, h, of Wile E. above the ground t seconds after he releases the catapult is given by h(t) 4.9t^26+117t +42. Sketch graph on next page (2 points), scale (2 points), and label important points below (maximum, zeros, and y-intercept (4 points)).a) How high does he go (show algebraic support, 3 points)? ____________ b) Does Wile E. reach the roadrunner (1 point)? _________c) When is Wile E. at the same height as he was when he catapulted (show algebraic support, 3 points)? __________d) After how many seconds will Wile E. hit the ground (show algebraic support, 3 points)? _________e) Wile E. goes back to the Acme Company to get a stronger catapult. Catapults come in integer strengths; each increase of one meter per second initial velocity costs $100. How much will Wile E. have to pay for a catapult strong enough to reach the Roadrunner (explain reasoning or show work, 3 points)? ___________f) Since Wile E. has no extra money to buy more strength right now, he must think of another way to make this catapult work. What can he do (be as mathematically specific as possible, 3 points)?