Question

A ball is thrown vertically upward from the top of a building 1600 feet tall with an initial velocity of 80 ft per second. The distance d(t), in feet, of the ball from the ground after t seconds is d(t)=1600+80t-16t^2 . After how many seconds is the ball at its maximum height? Find the maximum height of the ball. How long will it take the ball to hit the ground?

Answer 1

• 1700 feet

• 12.81 seconds

Explanation:

Function given

• d(t)=1600 + 80t - 16t^2

Maximum height is the vertex of the parabola, which is achieved at:

• x = -b/2a

Substituting values of a and b

• x = -80/2*(-16) = 2.5

Value of d(2.5):

• d(2.5) = 1600 + 80*2.5 - 16*2.5^2 = 1700 ft

Time to hit the ground:

• 1600 + 80t - 16t^2 = 0
• t^2 - 5t - 100 = 0

Solving we get positive root:

• t = 12.81 seconds