The height of a projectile fired upward is given by the formula s = v0t − 16t2,
where s is the height in feet,
v0
is the initial velocity, and t is the time in seconds. Find the time for a projectile to reach a height of 96 ft if it has an initial velocity of 128 ft/s. Round to the nearest hundredth of a second.

The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Step-by-step explanation:

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

Where s is the height in feet, v₀ is the initial velocity, and t is the time in seconds.

Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.

In other words, given that v₀ = 128, find t such that s = 96.

Substitute:

This is a quadratic. First, we can divide both sides by -16:

Isolate the equation:

The equation isn't factorable, so we can consider using the quadratic formula:

In this case, a = 1, b = -8, and c = 6. Substitute:

Simplify:

Hence, our two solutions are:

So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.