I need help plzz

Question

The function  defined by  models the height, in meters, of an object  seconds after it is dropped from a helicopter.  

From what height is the object dropped? Explain your reasoning.

Answer 1

Hi James H.,

First of all, please check your text before you submit it. You meant (I hope) "h(t) =" , NOT "h(t) +". That's a problem easily overcome in this context, but it won't always be that way.

So, you are left with an equation for height as a function of time. What would be the logical assignment for the drop time, if t is defined as "seconds after it is dropped"? In other words, with what event does the "t-clock" start running? So you have a value. Plug it into the equation, and calculate!

There's something else you should have noticed about the equation. You could quite easily pull a multiplication factor of 4.9 out of the first term in the right side, to get: h(t) = 4.9 * (10 + t ) * (10 - t ) . Now you can easily see the symmetry of the quadratic equation which is set up (in factored form, already!) and observe (I hope) that the parabolic trajectory would have intercepts (launch and impact times) of -10 and 10 sec for an equivalent ground-launched object.

Now consider one other manipulation of the equation. If you re-defined height as vertical upwards from the helicopter location, the equation becomes h(t) = 4.9 * ( -t² ) . In short, h = -(1/2)gt² . Does that look familiar?

--Cheers, --Mr. d.