Question

Aviation A helicopter hove 40 ft above the ground. Then the helicopter climbs at a rate of 21 ft/s. Write a rule that represents the helicopter's height h above the ground as a function of time t. What is the helicopter's height after 45 s?

Answer 1

`h_t=40+21t`

`h_(45)=40+(21xx45)" "=" "985 feet`

Explanation:

Let height increase be positive value
Let height decrease be negative value
Let time in seconds be ..............................`t`
Let height in feet at any time `t` be ............`h_t`

`color(brown)("Initial condition")" "-> height =40 feet`

Given: height increase rate is 21 feet per second `->21 (ft)/s`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Building the equation")`

After 1 second the height increases by 21 feet
After 2 seconds the height has increased by `21+21` feet
After 3 seconds the height has increased by `21+21+21` feet

So after `t` seconds the height has `ul("changed")` by `21xxt`

So we have:

height at t seconds = initial height + change in height upwards

`" "color(blue)(h_t=40+21t)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine height after 45 seconds")`

So for 45 seconds we have:

Note that height at 45 seconds is written as `h_(45)`

`" "color(blue)(h_(45)=40+(21xx45)" "=" "985 feet)`