Quadratic Formula

Question

A basketball is thrown toward a hoop, which is 3m above the ground. The height (y, in metres) if the basketball above the ground after t seconds is given by the equation y= -5t^2 + 10t +2

A) the shot misses and the ball hits the floor. What was the hang time of the ball (that is, after how many seconds does the ball hit the ground)?

b) The player makes the she shot. How much time has passed between the throwing and the scoring

1. Be careful when choosing which number is the solution. The ball first reaches a height of 3m as it is traveling upwards.

Answer 1

(A)

Set y=0 and solve for t using the quadratic formula. You will get a negative and a positive solution. Since time starts at t=0, the positive solution is the correct one.

(B)

Set y=3 (the height of the hoop) and solve for t.

-5t² + 10t + 2 = 3

-5t² + 10t - 1 = 0

Again, solve for t using the quadratic formula. You will get 2 positive solutions. The lower solution is the time to reach the height of the hoop on the way up. The higher solution is the time to reach the height of the hoop on the way down. The latter is the answer for (B).