A projectile is launched straight up from the ground with an initial velocity of 120ft/s If acceleration due to gravity is - 16ft/s^2 after about how many seconds will the object reach a height of 200 ft? h(t)=at^2+vt+h_(0) 1:0 s 1.7 s 2.5 s 8.0 s

## Step1: Identify the known and unknown variables### The given initial velocity is , the height to reach is , and the acceleration due to gravity is . We need to determine the time .## Step2: Write the height equation### The height equation for projectile motion is \( h(t) = a t^2 + v_0 t + h_0 \). Here since the object is launched from the ground level.## Step3: Substitute the known values into the height equation### Substitute , , , and into the equation: ## Step4: Solve the quadratic equation### Rearrange the equation to standard quadratic form: Divide the entire equation by 4 for simplicity: Use the quadratic formula where , , and :Calculate the discriminant: Find the roots: This gives two solutions: ## Step5: Select the feasible time### Since 5 seconds seems impractically long for the object to ascend and still be rising, select the smaller, realistic time value.#