Use the position function to write a model

Question

A varsity soccer player kicks a soccer ball approximately straight upward with an initial velocity of 50 ft/sec. The ball leaves the players foot at a height of 2 feet.

Part 1

Use the position function to write a model representing the height of the soccer ball (in feet) t seconds after being kicked. (Assume the acceleration due to gravity is 32 ft/sec2). Be sure to reduce your first term.

Part 2

Use that model to determine the times at which the ball is 36 feet in the air. Use FACTORING to solve. Be sure to write a sentence that explains both of your answers.

Answer 1

(1)

h(t) = -16t² + 50t + 2

(2)

Set h(t)=36 and solve for t.

-16t² + 50t + 2 = 36

-16t² + 50t - 34 = 0

Solve for t using the quadratic formula. You will get 2 positive solutions. The lower one is the time to reach 36 ft on the way up. The higher one is the time to reach 36 ft on the way down.