Question

A ball is thrown from a height of 110 feet with an initial downward velocity of 6/fts. The ball's height h (in feet) after t seconds is given by the following:

h=110-6t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.

Answer 1

The ball hits the ground approximately 3.79 seconds after it is thrown.

Step-by-step explanation:

To find when the ball hits the ground, we need to set the height h equal to zero and solve for t. So, we can set the equation 110 - 6t - 16t^2 = 0. This is a quadratic equation, and we can solve it using the quadratic formula.

Using the quadratic formula, we have t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = -6, and c = 110. Plugging in these values, we find two solutions: t = 3.79 seconds and t = 0.54 seconds.

Since we are interested in the time it takes for the ball to hit the ground, we take the longer solution, which is t = 3.79 seconds.