# Thread: free fall story problem

1. ## free fall story problem

A rescue package is being dropped out of a helicopter to a stranded group 400 ft below with an approximate angle of depression of 75 degrees. The falling object is at 337.94 ft 2 seconds after leaving the helicopter. It hits the ground at 5.0304 seconds. Create a function that models the height of the package over time.
What type of function would I use for this problem?

2. Originally Posted by Chica513
A rescue package is being dropped out of a helicopter to a stranded group 400 ft below with an approximate angle of depression of 75 degrees. The falling object is at 337.94 ft 2 seconds after leaving the helicopter. It hits the ground at 5.0304 seconds. Create a function that models the height of the package over time.
What type of function would I use for this problem?
I can't see how this is a "free-fall" problem as the acceleration of the object is not g. Here's how I would approach this.
We can assume that the acceleration is constant, so we can model the height as
$\displaystyle h(t) = h_0 + v_0t - (1/2)at^2$

We can typically take h0 to be the height at ground level, so set h0 = 0 ft. Then we have
$\displaystyle h(t) = v_0t - (1/2)at^2$

You know that
$\displaystyle h(2) = 337.94 = v_0(2) - (1/2)a(2^2)$

and
$\displaystyle h(5.0304) = 0 = v_0(5.0304) - (1/2)a(5.0304^2)$

We have two simultaneous equations in v0 and a.

-Dan