# The End of the Ski Jump - Optimizing Launch Angle

## Homework Statement

A ski jumper leaves the ski track moving in the horizontal direction with a speed of 25.0 m/s as shown in Figure 4.14. The landing incline below her falls off with a slope of 35.0°. Where does she land on the incline? I've attached an image of the problem, my work is below it.

## Homework Equations

xf = (Vicos(theta))t = dcos(phi)
yf = (Visin(theta)t) - (0.5)gt^2 = -dsin(phi)

## The Attempt at a Solution

I understand and reached the solution of part a), but I am struggling with part b). It says to eliminate time "t" and differentiate and maximize "d" in terms of angle "theta".

this is the furthest I've gotten:

xf = (Vicos(theta))t

t = xf/(Vicos(theta))

yf = (Visin(theta))t - (0.5)gt^2

plugging in t = xf/(Vicos(theta))

yf = (Visin(theta))(xf/(Vicos(theta)) - (0.5)g(xf/(Vicos(theta))^2
= xftan(theta) - (0.5)g(xf/(vicos(theta))^2
= xftan(theta) - xf^2(1/(2gVi^2cos^2(theta))

(factoring out and dividing by xf)

yf/xf = tan(theta) - xf/(2gVi^2cos^2(theta))

-dsin(phi)/(dcos(phi)) = tan(theta) - xf/(2gVi^2cos^2(theta))

-tan(phi) = tan(theta) - xf/(2gVi^2cos^2(theta))

I don't know what to do after this step. Any help would be greatly appreciated. Thank you!

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haruspex
Homework Helper
Gold Member
xf = (Vicos(theta))t
What does theta represent in that equation? Think carefully.

What does theta represent in that equation? Think carefully.
Hi Haruspex, I believe it represents the launch angle

haruspex
Homework Helper
Gold Member
Hi Haruspex, I believe it represents the launch angle
Yes, but angle to what?

Edit: sorry, forget it..... may have misread something. More soon....

Yes, but angle to what?

Edit: sorry, forget it..... may have misread something. More soon....
The angle in respect to the x-axis? Is it because it's initially at zero? Because φ is 35 degrees ... ?

Yes, but angle to what?

Edit: sorry, forget it..... may have misread something. More soon....

haruspex
Homework Helper
Gold Member
= xftan(theta) - (0.5)g(xf/(vicos(theta))^2
= xftan(theta) - xf^2(1/(2gVi^2cos^2(theta))
Check that step. The second line is dimensionally inconsistent.
(This is a useful technique for finding algebraic errors in physics. Check whether the final equation makes sense dimensionally. If it doesn't, do a 'binary chop' to see where it went wrong.)

Bdhillon1994
Check that step. The second line is dimensionally inconsistent.
(This is a useful technique for finding algebraic errors in physics. Check whether the final equation makes sense dimensionally. If it doesn't, do a 'binary chop' to see where it went wrong.)
Okay thanks, I'll review my work once I'm home. Also, what do you mean by "binary chop"?

haruspex