The height of a projectile fired upward is given by the formula

Different initial up speed but use :

http://www.jiskha.com/display.cgi?id=1396965991#1396965991.1396967805

if Sam fires a bullet straight upward with an initial velocity of 128 ft/sec, the height h of the bullet above the ground t sec after it is fired can be modeled by the equation h(t)=-16(t-4)^2+259

To find the time for the projectile to return to Earth, we need to find the value of t when the height, s, is equal to zero.

The formula for the height of the projectile is given as:
s = v0t - 16t^2

If the projectile returns to Earth, its height will be zero, so we can set s = 0 and solve for t.

0 = v0t - 16t^2

Rearranging the equation, we have:
16t^2 = v0t

Divide both sides of the equation by t:
16t = v0

Now, substitute the given value for the initial velocity, v0 = 184 ft/s:
16t = 184

Divide both sides of the equation by 16:
t = 184/16

Simplifying the right side of the equation:
t = 11.5

Therefore, the time for the projectile to return to Earth is 11.5 seconds.

To find the time for a projectile to return to Earth, we need to solve the equation s = v0t - 16t^2 for t, where s is the height and v0 is the initial velocity.

In this case, the projectile is returning to Earth, so the height will be 0. Therefore, we can rewrite the equation as:
0 = v0t - 16t^2

Let's plug in the given initial velocity, v0 = 184 ft/s:
0 = 184t - 16t^2

This is a quadratic equation in terms of t. We can now use the quadratic formula to solve for t. The quadratic formula states:
t = (-b ± √(b^2 - 4ac)) / (2a)

Comparing our equation with the standard quadratic form (ax^2 + bx + c = 0), we have:
a = -16, b = 184, and c = 0.

Substituting these values into the quadratic formula, we get:
t = (-184 ± √(184^2 - 4*(-16)*0)) / (2*(-16))

Simplifying further:
t = (-184 ± √(33856)) / (-32)

Finally, solving for t gives us two possible solutions:
t = (-184 + √(33856)) / (-32)
t = (-184 - √(33856)) / (-32)

Calculating these values will give us the times for the projectile to return to Earth.