Question

The height of a ball thrown upward is given by h(t) = -2t² + 12t - 10 meters, where t is in seconds. What is the velocity of the ball when it returns to the ground? 1) -8 m/s 2) -10 m/s 3) 8 m/s 4) 10 m/s

Answer 1

The velocity of the ball when it returns to the ground is -10 m/s.

Step-by-step explanation:

The height of the ball is given by the equation h(t) = -2t² + 12t - 10. To find the velocity when the ball returns to the ground, we need to find the time when h(t) = 0. Set h(t) = 0 and solve for t.

0 = -2t² + 12t - 10

Using the quadratic formula, we find two solutions: t = 0.54 s and t = 3.79 s. Since the ball is at ground level twice during its trajectory, we take the longer solution of t = 3.79 s. Now, we can find the velocity v(t) when t = 3.79 s by taking the derivative of h(t) with respect to t.

v(t) = -4t + 12

Substituting t = 3.79 s into the equation yields v(t) = -4(3.79) + 12 = -15.16 + 12 = -3.16 m/s. Therefore, the correct answer is 2) -10 m/s.