Question

A ball is thrown upward with an initial velocity of 11 meters per second. Suppose that the initial height above the ground is 6 meters. At what time will the ball hit the ground? The ball is on the ground when s=0. Use the equation s=-5t²+vt+h

A) 2 seconds
B) 3 seconds
C) 4 seconds
D) 5 seconds

Answer 1

The time at which the ball will hit the ground is found by solving the quadratic equation for s = 0, using the initial velocity and height given. The positive time solution of this equation is 2 seconds, which is the answer to the question.

Step-by-step explanation:

To determine when the ball will hit the ground, we can use the quadratic equation given for the vertical motion of the ball:

s = -5t² + vt + h

Solving for "s = 0", since that represents the ball being on the ground, we would set up the equation as follows:

0 = -5t² + (11 m/s)t + 6 m

To find the time "t" when the ball hits the ground, you can use the quadratic formula. However, since the equation is already given in a format where you can identify the coefficients, you can solve it directly:

-5t² + 11t + 6 = 0

Using the quadratic formula, we can find the two possible times that the ball will be on the ground. When performing the calculations, the relevant (positive) time that it returns to the ground is found to be "t = 2 seconds".

Therefore, the correct answer is A) 2 seconds.