Question

It is desired to design a ski jump ramp. The ramp will be represented by a polynomial whose graph is a side view of the ramp. The ramp must fulfill the following specifications:

The ramp begins at a height of 100 feet and ends at a height of 10 feet above the ground.
From start to finish, the ramp covers a horizontal distance of 120 feet.
 A skier will leave horizontally, and must fly at the end of the ramp at an angle of 30 ° above the horizontal.

1. Based on the specifications, determine the degree of the polynomial used, and determine the equations corresponding to the data.

I only need to know the degree of the polynomial so I can complete the rest of the homework
Thank You!

Answer 1

well, you only have two points, so a line would suffice to join them.

But, as the slope at the end of the ramp is not 90/120, that gives another constraint. That's like specifying a third point. So, use a quadratic to model the ramp.

y = ax^2+bx+c
y(0) = 100, so c=100
y(120) = 10, so 14400a+120b+100 = 10
y' = 2ax+b
y'(120) = 1/√3, so 240a+b = 1/√3

Now you can solve for a and b.