Problem 1059

A baseball is dropped from a stadium seat that is 83 feet above the ground. Its height s in feet after t seconds is given by s(t) = 83 = 16t2. Estimate how long it takes from the baseball to strike the ground.

Solution:-

Use the given information  to write a quadratic equation.

To find the time, notice that the position of the ball when it hits the grounds is s(t) = 0.

To solve the quadratic equation 0 = 83 – 16t2, notice that there is an t2 –term but not an t-term.

That means the square root method would be easy to use to solve the equation. Begin by isolating the t2-term.

0 = 83 – 16t2

16t2 = 83

t2  =

The square root property states that if k is nonnegative number, then the solutions to the equation x2 = k are given by ± .

Apply the square root property.

t2  =

t = ±

Evaluate the radical. Round the result to the nearest tenth.

2.3 , -2.3

Finally, interpret this result in the context of the problem. The solution of 2.3 has no meaning in this problem because the variable t corresponds to time. Therefore, it takes approximately 2.3 seconds for the baseball to strike the ground.