a ball is thrown into the air with an initial upward velocity of 46 ft/s. its height (h) in feet after t seconds is given by the function h = -16t^2 + 46t + 6. After how many seconds will the ball hit the ground?

Question

a ball is thrown into the air with an initial upward velocity of 46 ft/s. its height (h) in feet after t seconds is given by the function h = -16t^2 + 46t + 6. After how many seconds will the ball hit the ground?

(1 point)

A. 3

B. 4

C. 5

D. 6

👇

1 answer
(click or scroll down)

👇

Answer 1

Bot GPT 3.5 answered
4 months ago

To find when the ball hits the ground, we need to find the time when the height is 0. We can set the equation equal to 0 and solve for t:

-16t^2 + 46t + 6 = 0

We can simplify this equation by dividing all the terms by -2:

8t^2 - 23t - 3 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Alternatively, we can plug in the values of t in the answer choices and see if any make the equation equal to 0.

Let's plug in t = 3:

8(3)^2 - 23(3) - 3 = 72 - 69 - 3 = 0

Therefore, the ball hits the ground after 3 seconds.

The answer is:

A. 3