Question

A bird is flying on the path: h = 330 - 24t. Harry hits a golf ball with a path: h= -4.9t² +93t+0.5. Does Harry hit the bird with the ball? If yes, what time does it hit the bird (round to the nearest tenth).

Answer 1

By equating the height equations of the bird's flight and the golf ball's trajectory, and solving the resulting quadratic equation, it is determined that Harry could potentially hit the bird with the golf ball at approximately 3.8 seconds after the ball is hit.

Step-by-step explanation:

To determine if Harry hits the bird with the golf ball, we must find the point in time when both the bird and the golf ball occupy the same height. The bird's flight path is given by h = 330 - 24t, and the trajectory of the golf ball is given by h = -4.9t² + 93t + 0.5. To solve this problem, we equate the two height equations and solve for t.

330 - 24t = -4.9t² + 93t + 0.5

Upon rearranging and combining like terms, we get:

4.9t² - 117t + 329.5 = 0

Using the quadratic formula, t = (-b ± √(b² - 4ac))/(2a), yields two possible solutions t = 3.79 s and t = 0.54 s. As the golf ball reaches a height of 10 m twice during its trajectory (on the way up and on the way down), we select the longer solution for the time at which the ball could potentially hit the bird, assuming it also crosses the bird's flight path at this time.

Therefore, Harry could potentially hit the bird with the golf ball at approximately 3.8 seconds after the ball is hit.