Question

If an object is dropped from a height of 116 feet, the function h(t)=-16t^2+116 gives the height after t seconds. When will the object hit the ground?

Answer 1

Answer:

2.69 seconds

Step-by-step explanation:

the function for the height and time is:

$h(t)=-16t^2+116$

when the object collides with the ground, it means that at that moment its height is zero. So we need to solve the equation above for when h(t) equals zero:

$0=-16t^2+116$

clearing for t:

$-116=-16t^2\\\frac{-116}{-16}=t^2\\ 7.25=t^2\\\sqrt{7.25}=t\\ 2.69=t$

the object will hit the ground at time 2.69 seconds

Answer 2

Let h(t)= 0 (because when it reaches the ground h=0)

0=-16t^2+116
16t^2=116
divide both sides by 16
t^2= 7.25
square root both sides to find t
t=2.69sec