Question

An object is dropped from a height of 400 feet off the ground. The height "h" of the object after "t" seconds can be found using the equation h=400-16t^2

- When will the height be 144 feet?
- When will the object reach the ground?

Answer 1

Dropped from 400 feet, the object takes 4 seconds to reach a height of 144 feet and 5 seconds to hit the ground.

Object's Falling Height

The provided information describes the falling object's height using the formula:

`h(t) = 400 - 16t^2`

where:

h(t) is the height of the object in feet after t seconds , 400 is the initial height of the object in feet ,t is the time in seconds.

Finding the Time When the Height is 144 feet

To find when the height reaches 144 feet, we need to solve the equation for t when h(t) = 144:

`144 = 400 - 16t^2\\16t^2 = 256\\t^2 = 16`

t = ±4

Since the object cannot go back up, we take the positive value:

t = 4 seconds

Therefore, the object will be 144 feet high after 4 seconds.

Finding the Time When the Object Reaches the Ground

The object reaches the ground when its height becomes 0 (h(t) = 0):

`0 = 400 - 16t^2\\16t^2 = 400`

`t^2 = 25`

t = ±5

Again, we only consider the positive value:

t = 5 seconds

Therefore, the object will reach the ground after 5 seconds.