The height of an object projected straight upward with an initial speed of 1000 meters/second is given by h(t)=1000 t-4.9t^2

Question

when does the object land?

What are the zeros of h(t)?

Does this function have an inverse?

Answer 1

To find out when the object lands, we set h(t) equal to zero.

 

0 = 1000t - 4.9t²

 

 

We can factor the right side of equation.

 

0 = t(1000 - 4.9t)

 

t=0        and         1000 - 4.9t = 0

 

                                   -4.9t = -1000

 

                                         t = 204.082

 

 

We reject t=0.  So the object lands in 204.082 seconds.

 

 

We already found the zeros from the first part.

 

 

The given function is a parabola.  If we can get a reflection this over the line y=x, then the function is an inverse.

 

Answer 2

For part A, we want to know when the height is 0. We can factor out a t to make it easier to see.

 

h(t) = t (1000 - 4.9t)

 

When it this 0? t=0 is an obvious choice, because when the first t=0, the result is 0. The less obvious answer is when (1000 - 4.9t) = 0. We find another value for t from this part. This is when the object lands.

 

t_land = 1000/4.9

 

Part B asks the same things as part A. Our zeroes are when t = 0 and when t = 1000/4.9

 

Part C asks if this equation has an inverse. What is the test to find if the equation has an inverse function? It is the horizontal line test. If you draw a horizontal line (that's a line that spans all of x at one y value), how may times does it cross the function? If the answer is more than one, it fails the test and does not have an inverse function.

 

We find that this function fails the horizontal line test - therefore it does not have an inverse function.