Question

A person standing close to the edge on top of a 133-foot building throws a baseball vertically upward. The quadratic function s(t)=-16t^{2} +64t+133 models the ball’s height above the ground, s(t), in feet,

t seconds after it was thrown.

Question: After how many seconds does the ball reach the ground? Round to the nearest tenth of a second if necessary.

A) 1.4 seconds
B) 2.1 seconds
C) 3.0 seconds
D) 3.5 seconds
E) 4.2 seconds

Answer 1

The ball takes approximately 3.8 seconds to reach the ground.

Step-by-step explanation:

The quadratic function s(t)=-16t^2 +64t+133 models the height, in feet, of the ball above the ground at time t seconds after it was thrown.

To find the time it takes for the ball to reach the ground, we need to determine when the height is equal to zero.

We can do this by setting the quadratic function equal to zero and solving for t.

Using the quadratic formula, we find two possible solutions: t = 3.79 seconds and t = 0.54 seconds.

Since the ball is at a height of 10 feet twice during its trajectory, we choose the longer solution, which is t = 3.79 seconds.

Therefore, the ball takes approximately 3.8 seconds to reach the ground.