A soccer player kicks a ball and gives it an initial upward velocity of 47 feet per second. If everyone waits for the ball to bounce, how long will it be in the air? (Use the vertical motion formula, h= -16tsquared + vt + c, where h is the height of the ball will be at time t, v is the initial upward velocity, and c is the starting height.

PLEASE HELP! I DON'T UNDERSTAND!

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the ball will bounce when its height returns to zero. Use the given equation, plugging in the initial height and velocity

h = -16t^2 + 47t
= t(-16t+47)

clearly h=0 when t=0 (the ball is kicked) and t=47/16 (the ball bounces)

So, the ball is in the air 47/16 seconds.

To determine how long the ball will be in the air, we need to find the time when the height of the ball is 0. In this case, the ball starts on the ground, so the starting height, c, is 0.

The vertical motion formula for the height of an object is given by:

h = -16t^2 + vt + c

where:
h = height of the object at time t
t = time (in seconds)
v = initial upward velocity
c = starting height

In this case, we know the initial upward velocity is 47 feet per second, so v = 47. The formula becomes:

h = -16t^2 + 47t

We can set h = 0, since we want to find the time when the height is 0:

0 = -16t^2 + 47t

Now, we can solve this quadratic equation for t. One way to solve it is by factoring, but in this case, it's easiest to use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = -16, b = 47, and c = 0. Plugging in these values, we get:

t = (-47 ± √(47^2 - 4*(-16)*0)) / 2*(-16)

Simplifying further:

t = (-47 ± √(2209)) / (-32)

Now, we calculate the value inside the square root:

√(2209) = 47

Plugging that back into the equation:

t = (-47 ± 47) / (-32)

Simplifying further gives us two values for t:

t1 = 0
t2 = 3.718

Since time can't be negative, we discard t1 = 0. Therefore, the ball will be in the air for approximately 3.718 seconds.

Note: The answer is rounded to three decimal places.