a punter kicked the football into the air with an upward velocity of 62 ft/s. Its height h in feet after t seconds is given by the function h= -16t ^2 + 62 t + 2. How long does it take for the ball to hit the ground?

@Henry, you are no help. I saw Amy's previous post *I know this was 7 years ago* and you answered it incorrectly.

The answer is B. 1.94 s, 62.06 ft

To find the time it takes for the ball to hit the ground, we need to determine the value of "t" when the height "h" is equal to zero.

Given the equation h = -16t^2 + 62t + 2, we can set h to zero:

0 = -16t^2 + 62t + 2

Next, we can solve this quadratic equation using either factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In our equation, we have a = -16, b = 62, and c = 2:

t = (-(62) ± √((62)^2 - 4(-16)(2))) / 2(-16)

Simplifying further:

t = (-62 ± √(3844 - (-128))) / -32

t = (-62 ± √(3972)) / -32

t = (-62 ± √(9 * 441)) / -32

t = (-62 ± 9√(441)) / -32

t = (-62 ± 9 * 21) / -32

Now, we have two possible solutions:

t = (-62 + 189) / -32
t = (127) / -32
t = -3.97

t = (-62 - 189) / -32
t = (-251) / -32
t = 7.84

Since time cannot be negative, we discard the negative solution.

Therefore, it takes approximately 7.84 seconds for the ball to hit the ground.

To find out how long it takes for the ball to hit the ground, we need to determine the time when the height (h) is equal to zero. In other words, we need to solve the equation:

-16t^2 + 62t + 2 = 0

To solve this equation, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = -16, b = 62, and c = 2.

Substituting these values into the quadratic formula, we get:

t = (-62 ± √(62^2 - 4(-16)(2))) / (2(-16))

Simplifying further:

t = (-62 ± √(3844 + 128)) / (-32)

t = (-62 ± √(3972)) / (-32)

Now, let's calculate the square root of 3972:

√3972 ≈ 63.02

This gives us two possible solutions:

t₁ = (-62 + 63.02) / (-32) ≈ 0.04 seconds

t₂ = (-62 - 63.02) / (-32) ≈ 1.97 seconds

Since time cannot be negative in this context, we can discard the negative solution. Therefore, the ball takes approximately 1.97 seconds to hit the ground.

See your previous post.