Question

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled using h(t) = 144 – 16t2.

How many seconds will it take the object to reach the ground?

Answer 1

Answer: *For 2 being an exponent*: 3 seconds

*For 2 being multiplied to t* : 4.5 seconds

Explanation:

*For 2 being an exponent*

It says we want to know the time it will take to reach the ground. This means that the height will be 0 at this time.

So we can set h(t) = 0 and solve for t.

`0 = 144 - 16t^2`

Subtract 144:
`-144 = -16t^2`

Divide -16:
`9 = t^2`

Now square root:
`3 = t`

So it will take 3 seconds to reach the ground.

*For 2 being multiplied to t*

It says we want to know the time it will take to reach the ground. This means that the height will be 0 at this time.

So we can set h(t) = 0 and solve for t.

`0 = 144 - 16t2`

We can simplify by multiplying the -16 and 2:
`0 = 144 - 32t`

Subtract 144:
`-144 = -32t\\`

Divide by -32: 4.5 = t

So it will take 4.5 seconds to reach the ground.