Question

A smart-phone is thrown upwards from the top of a 240-foot building with an initial velocity of 32

feet per second. The height h of the smart-phone after t seconds is given by the quadratic equation
h = - 16t2 + 32t + 240. When will the smart-phone hit the ground?

Answer 1

t = 5 sec

Step-by-step explanation:

h = - 16t² + 32t + 240

On the ground h = 0.

- 16t² + 32t + 240 = 0 / : (- 16)

t² - 2t - 15 = 0

(t-5)(t+3) = 0

t = 5, t = - 3

Time can be only positive, so t = 5 sec

Answer 2

A smart-phone is thrown upwards from the top of a 240-foot building with an initial velocity of 32 feet per second, the smart-phone will hit the ground after 5 seconds.

Step-by-step explanation:

To find when the smart-phone will hit the ground, we need to set the height equation h = -16t² + 32t + 240 to 0, since the height when it hits the ground is 0.

So, we have the equation -16t^2 + 32t + 240 = 0.

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

Let's use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

t = (-b ± sqrt(b² - 4ac)) / (2a)

For our equation, a = -16, b = 32, and c = 240.

Plugging in these values, we get:

t = (-32 ± sqrt(32² - 4(-16)(240))) / (2(-16))

Simplifying further, we have:

t = (-32 ± sqrt(1024 + 15360)) / (-32)

t = (-32 ± sqrt(16384)) / (-32)

t = (-32 ± 128) / (-32)

Finally, we can simplify to find the two solutions:

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

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

Since time cannot be negative in this context, so therefore the smart-phone will hit the ground after 5 seconds.