A projectile is launched from ground level with an initial velocity of v_(0) feet per second. Neglecting air resistance, its height in feel i seconds after laut given by s=-16t^2+v_(0)t Find the time(s) that the projectile will (a) reach a height of 64 ft and (b) return to the ground when v_(0)=80 feet per second. (a) Find the time(s) that the projectile will reach a height of 64 ft when v_(0)=80 feel per second. Select the correct choice below and, if necessary, fill in answer box to complete your choice. OA. square seconds (Use a comma to separate answers as needed.) B. The projectile does not reach 64 feet (b) The projectile returns to the ground after square second(s)

## Step 1: Formulate the equation for height ### Given .### Plug in : .## Step 2: Solve for time when ### Set . ### Rearrange: .## Step 3: Solve quadratic equation### Use quadratic formula , where , , and .### Calculate discriminant: \( b^2 - 4ac = 80^2 - 4(-16)(-64) = 6400 - 4096 = 2304 \).## Step 4: Find times ### Calculate \( t = \frac{-80 \pm \sqrt{2304}}{2(-16)} = \frac{-80 \pm 48}{-32} \).### Solve for and : , .## Step 5: Find time to return to ground ### Set .### Factor: \( t(-16 t + 80) = 0 \).### Solve for or (since is initial launch time).#