How much time passes before the cap hits the ground?

Graduate students throw their graduation caps into the air to convey their hopes and aspirations for a future career. The height, h(t), in feet of the cap in the air t seconds after it is thrown can be modeled by the function:

h(t) = −16t^2 + 32t+ 4

1 Answer
Apr 12, 2018

Exact answer: x=1+sqrt5/2 " s"

Explanation:

To find the time at which the cap hits the ground, the height must be equal to 0:

So by setting the height equal to 0, we get:
-16t^2+32t+4=0

Solve it as a quadratic:
Factor with GCF:
-4(4t^2-8t-1)=0

It is not possible to factor further so let's use the quadratic formula:
x=(-b+-sqrt(b^2-4ac))/(2a)

x=(8+-sqrt(64-4(4)(-1)))/(2(4))

x= (8+-4sqrt(5))/8

x=1+-1/2sqrt5 " s"

Since time can't be negative:
x=1+sqrt5/2 " s"

graph{-16x^2+32x+4 [-91.7, 53.6, -21.14, 51.5]}