Velocity Word Problem

Question

An arrow ia fired straight up from the ground with an initial velocity of 240 feet per second. Its height, s(t), in feet at any time is given by the function s(t) = -16t^2 + 240t. Find the interval of time for which the height of the arrow is greater than 576 feet.

Answer 1

There are two methods you can use to solve this question:

 

1) Plot the question on a graph if you have a calculator and see at which time the parabola hits 576ft on its way up and then again when it reaches that number on its way down.

 

2) The second way you can solve this problem is to use the quadratic formula.

 

We initially have the equation of s(t) = -16t^2 +240t

 

Since we want to know when the arrow reaches a height of 576 feet, we are going to go ahead and set s(t) to 576.

 

This gives us...    576 = -16t^2 + 240t

 

To use the quadratic formula, we are going to have to rearrange this equation a little bit by subtracting 576 from both sides.

 

-16t^2 + 240t - 576 =0

 

Now we can plug the values into the quadratic formula, with a = -16; b = 240 and c = -576.

 

When we plug these values into the quadratic formula, we get two answers, which are t=3 and t=12.

 

This tells you that on the way up, the arrow reached a height of 576 feet at 3 seconds and then dropped back below that level at 12 seconds, for a total of 9 seconds above that height.

Answer 2

Solve the quadratic equation s(t) = 576.  There should be two roots ('zeroes').

 

Between those t values, the height will exceed 576, since this graph is a parabola that opens downwardly.