Physics is not nice

Question

A ski jumper travels down a slope and leaves the ski track moving in the horizontal direction with a speed of 28 m/s as in the figure. The landing incline below her falls off with a slope of θ = 46◦ . The acceleration of gravity is 9.8 m/s. Calculate the distance d she travels along the incline before landing. Answer in units of m.

Answer 1

It takes a number of steps to get the answer here.

First, recognize that the distance (d) down the 46 degree slope forms the hypotenuse of a right triangle with the horizontal distance (x) = (28 m/s)t (from v = x/t), and the vertical distance (y) = 4.9t² (from y = 0.5gt²).

We can also write trig equations for the sides using the slope of 46 degrees: cos 46 = 0.695 = x/d and sin 46 = 0.719 = y/d.

Now substitute in the previous values for x and y: 0.695 = 28t/d and 0.719 = 4.9t²/d. We now have two equations and two unknowns so solve one equation for t then substitute into the other: t = 0.695d/28 = 0.248d then 0.719 = 4.9(0.248d)²/d ; 0.719 = 0.003d ;

d = 238 m.