A projectile is launched vertically upward from the top of a 240-foot building. This translates to the model

y = -16t^2 + 32t + 240 where y is the height in feet and t is the time in seconds after it was launched, When will the projectile hit the ground?

Duplicate post. See my previous answer.

I wanted to say thank you very much this helps lots

To find the time when the projectile hits the ground, we need to set the height (y) to zero and solve for t in the equation:

y = -16t^2 + 32t + 240

Setting y = 0:

0 = -16t^2 + 32t + 240

Now we can solve for t by factoring or using the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 32, and c = 240. Substituting these values into the formula:

t = (-32 ± √(32^2 - 4(-16)(240))) / (2(-16))

Simplifying inside the square root:

t = (-32 ± √(1024 + 15360)) / (-32)

t = (-32 ± √(16384)) / (-32)

t = (-32 ± 128) / (-32)

Now we have two possible solutions:

1. t = (-32 + 128) / (-32)
t = 96 / -32
t = -3

2. t = (-32 - 128) / (-32)
t = -160 / -32
t = 5

Since time cannot be negative in this case, we discard the first solution (-3). Therefore, the projectile will hit the ground after 5 seconds.

To determine when the projectile will hit the ground, we need to find the time at which the height y becomes zero.

Given the equation y = -16t^2 + 32t + 240, we can set y equal to zero:

0 = -16t^2 + 32t + 240

Now we have a quadratic equation. We can use the quadratic formula to solve for t:

t = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = -16, b = 32, and c = 240. Plugging these values into the quadratic formula, we get:

t = (-32 ± √(32^2 - 4(-16)(240))) / (2(-16))

Simplifying this expression further, we have:

t = (-32 ± √(1024 + 15360)) / -32

t = (-32 ± √(16384)) / -32

t = (-32 ± 128) / -32

Now we have two possible solutions for t:

t1 = (-32 + 128) / -32 = 96 / -32 = -3

t2 = (-32 - 128) / -32 = -160 / -32 = 5

Since time cannot be negative in this context, we ignore the negative solution.

Therefore, the projectile will hit the ground after 5 seconds.