Question

A ball is thrown from the top of a tall building. The distance, in feet, between the ball and the ground t seconds after the ball is thrown is given by d(t) = -6t^2 + 10t + 34. How long after the ball is thrown is it 10 ft from the ground?

A. t = 1 second
B. t = 2 seconds
C. t = 3 seconds
D. t = 4 seconds

Answer 1

Solving the quadratic equation -6t^2 + 10t + 34 = 10 and discarding the negative value, we find that the ball is 10 ft from the ground after 3 seconds.

Step-by-step explanation:

To determine how long after the ball is thrown is it 10 ft from the ground, we need to set the distance function d(t) equal to 10 feet and solve for t. The equation given is d(t) = -6t^2 + 10t + 34. To find when the ball is at 10 feet, we solve the equation:

-6t^2 + 10t + 34 = 10

Subtract 10 from both sides of the equation:

-6t^2 + 10t + 24 = 0

Dividing the entire equation by -2 to simplify:

3t^2 - 5t - 12 = 0

Using the quadratic formula, we find that the equation yields two possible solutions for time: t = 3 and t = -4/3 seconds. Since time cannot be negative, the only reasonable answer is t = 3 seconds.