Word Problem

[rosy_peach]

I need help on getting started. How do i use the formulas given to me from the problem?

A sky diver jumped from an airplane and fell freely for several seconds before releasing her parachute. Her height, h, in meters about the ground at any time given by: h= -4.9t² + 5000 before she released her parachute, and, h= -4t + 4000 after she released the parachute.

How long after jumping did she release her parachute?
How high was she above the ground at that time?

 

[mmm4444bot]

It looks to me like the time variable is the same in both equations; there are no subscripts on t, as in t[sub:36dhn0ud]1[/sub:36dhn0ud] in one equation and t[sub:36dhn0ud]2[/sub:36dhn0ud] in the other.

So, think about the following.

Let's say, for example only, that the answer to the first question is t = 5 seconds. In other words, the skydiver opens the parachute 5 seconds after jumping out of the plane.

Then the height is given by -4.9t^2 + 5000 from t = 0 through t = 5 only.

This means that the other equation must take over from t = 5 onward.

So, the height is given by -4t + 4000 from t = 5 through t = whenever the skydiver lands.

In other words, at t = 5 seconds, both equations must give the exact height of the skydiver at exactly t = 5.

Does this give you any ideas about what to do with the two equations?

Here's another comment. In my example, once we had discovered that t = 5 is the instant when the two equations give the same height, we would then need to place constraints on the time domain for each, if we were to write down the overall definition for height.

We would do this by writing what's called a "piecewise function". Doing this shows everybody which equation applies for any given value of t.

h(t) = -4.9t^2 + 5000 when 0 <= t <= 5

h(t) = -4t + 4000 when t > 5

Of course, if the variables t and t in the equations that you posted are actually two different variables (one for elapsed time up to and including opening the parachute and a different one -- starting over at t = 0 -- for the elapsed time after opening the parachute), then there is not enough information to answer either question.

 

[Deleted member 4993]

I need help on getting started. How do i use the formulas given to me from the problem?

A sky diver jumped from an airplane and fell freely for several seconds before releasing her parachute. Her height, h, in meters about the ground at any time given by: h= -4.9t² + 5000 before she released her parachute, and, h= -4t + 4000 after she released the parachute.

How long after jumping did she release her parachute?
How high was she above the ground at that time?

Duplicate post:

http://www.mathhelpforum.com/math-help/ ... oblem.html