A woodland jumping mouse hops along a parabolic path given by y=-0.2x^2+1.3x where x is the mouse's horizontal position (in feet) and y is the corresponding height (in feet). Can the mouse jump over a fence 3 feet high? Explain.

Question

I know that x is 3.25 and the mouse's horizontal position in feet and I know that y is 2.1 (2.1125) and the corresponding height in feet. I don't understand how to tell if the mouse can jump over a fence that is three feet high. Could someone please explain this to me?

Answer 1

lets look at the graph.

You can plot the graph on your calculator, and see the max height of the mouse. If it is over 3, it can.

with calculus
finding the max
dy/dx=0=-.4x+1.3
x=1.3/.4=3.25
ymax=-.2(3.25^2)+1.3(3.25)=2.11 The mouse will smash into the fence.

Answer 2

What does the horizontal position mean?

Answer 3

Trains travel horizonally, rockets start off mostly vertical (up)

Horizonal means no elevation change.

Answer 4

So that's how far it has to jump and y is how high it can jump from that point to the fence?