assume that the maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. suppose that the car can go a maximum of 55 mph up a 5° hill, and a maximum of 104 mph down a 2° hill.
a) whats the equation for expressing maximum speed in terms of steepness?
b) what does the slope represent?
+118654 This is an interesting question :)
Assume that the maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. suppose that the car can go a maximum of 55 mph up a 5° hill, and a maximum of 104 mph down a 2° hill.
a) whats the equation for expressing maximum speed in terms of steepness?
Think of it like this.
Let k be the maximum speed on flat land - that when the angle is 0 degrees.
(0,k) is one point on the linear function.
If the angle is +5 degrees then the max speed is 55mph so (5, 55) is another point.
If the angle is -2 degrees then the max speed is 104mph so (5-2, 104) is another point.
Let the linear function be
\(S=m\theta+k\\ we\;\;have\\ 55=5m+k \qquad(1)\quad and\\ 104=-2m+k\qquad (2)\\ (1)-(2)\;\;gives\\ -49=7m\\ m=-7\\ \text{substituting back in we get}\\ k=90\\ \text{So the equatoin is}\\ S=-7\theta+90 \)
b) what does the slope represent?
The speed will drop by 7 mph for each 1 degree increase in the slope of the road.
Here is the graph that might help you understand
