Question

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A golf ball is launched straight up into the air from the ground with an initial velocity of 160 ft/s. The function that models the ball's height is: h(t) = -16t^2 + 160t.

a) Find how long it takes for the golf ball to reached its maximum height.

b) Determine how long the golf ball is in the air before it hits the ground.

c) Determine the maximum height that the golf ball reaches.

Answer 1

Answer:

• a) 5 sec
• b) 10 sec
• c) 400 m

Step-by-step explanation:

Given is the quadratic function:

• h(t) = -16t^2 + 160t

This gets maximum value at vertex, which is achieved at:

• x = -b/2a, of y = ax^2 + bx + c

In our case:

• t = -160/2(-16) = 5 seconds

Maximum height is at vertex:

• h(5) = -16*5^2 + 160*5 = 400 m

Time the ball hits the ground, h(t) = 0:

• -16t^2 + 160t = 0
• t^2 - 10t = 0
• t(t - 10) = 0
• t = 0 seconds is the starting point
• t = 10 seconds is when the ball hits the ground