A helicopter hovers 40 ft above the ground. Then the helicopter climbs at a rate of 21 ft/s. How do you write a rule that represents the helicopter's height #h# above the ground as a function of time #t#?

Question

Charles Anctil · Accepted Answer

# h = 21 t + 40#

If the helicopter climbs at a (constant) rate of #21 ft"/"s# then its distance at time #t# (relative to its starting point at height #40 ft# is given by:

#"speed"="distance"/"time" => "distance" = "speed" xx "time"#

Hence,

# \ \ \ h_("relative to height of 40 ft") = 21 * t#

# :. h_("relative to height of 0 ft") = 21 * t + 40#

# :. h = 21 t + 40#

Emma Aldridge · Answer

undefined The rule representing the helicopter's height $ h $ above the ground as a function of time $ t $ can be written as:

$$ h(t) = 40 + 21t $$

Where:
- $ h(t) $ represents the height of the helicopter above the ground at time $ t $.
- 40 represents the initial height of the helicopter above the ground.
- 21t represents the rate at which the helicopter is climbing, with $ t $ being the time in seconds.