Standing on a platform 60 feet high, a person accidentally fires a gun straight into the air. the formula h=-16t^2+100t+60 describes the bullet's height above the ground, h, in feet,t seconds after the gun is fired. how long will it take for the bullet to hit the ground? round to the nearest tenth on a second.

just set h=0 and solve for t:

t = 1/8 (25+√865) =~ 6.8 sec

To find out how long it will take for the bullet to hit the ground, we need to determine when the height, h, equals zero. In other words, we need to solve the equation -16t^2 + 100t + 60 = 0.

To solve this quadratic equation, you can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the equation.

In our case, a = -16, b = 100, and c = 60. Plugging these values into the quadratic formula, we get:

t = (-100 ± √(100^2 - 4(-16)(60))) / (2(-16))

Simplifying further:

t = (-100 ± √(10000 + 3840)) / (-32)
t = (-100 ± √13840) / (-32)

Now, we have two possible solutions for t: one with a positive square root and one with a negative square root. However, since time cannot be negative in this context, we can discard the negative solution.

We are left with:

t = (-100 + √13840) / (-32)

Calculating this, we get:

t ≈ 4.3

Therefore, it will take approximately 4.3 seconds for the bullet to hit the ground.