Question

A building is known to be 192 feet tall. A ball is dropped from the top of the building. In how many seconds will the ball hit the ground if the formula for the height of the ball at t seconds is given by h=192−16t2? Step 1 of 2 : First, what is the height of the ball when it hits the ground?

Answer 1

Answer:

• h = 0 when the ball hits the ground
• about 3.464 seconds

Step-by-step explanation:

The formula gives h = 192 when t=0, so we assume that h represents the height above the ground. The ball will have a height of 0 when it hits the ground.

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Using that in the equation, we can solve for t.

  0 = 192 -16t^2

  0 = 12 -t^2 . . . . . . divide by 16

  t^2 = 12 . . . . . . . . add t^2

  t = √12 = 2√3 ≈ 3.464 . . . . take the square root

It will take 2√3 seconds, about 3.464 seconds, for the ball to hit the ground.