Projectile Motion - Initial velocity

[airi]

1. The problem statement
A child runs down a hill with an angle of 20 degrees and then jumps up at a 20 degree angle above the horizontal. He lands 2.2m down the hill as measured along the hill. What is the child's initial velocity?

The Attempt at a Solution

Okay, I'm not even sure if I have my initial measurements right. This is a projectile problem right? With initial velocity unknown and a 40 degree angle (measured against the ground).

So, first I tried to find the time needed using Vxf=Vx0 + at.
-V0sin40 = Vosin40 - 9.8t
t= 2Vosin40/9.8

Then, i plug that into the Dy=Vy*t
2.2=(Vcos40)(2Vosin40 / 9.8)
10.78 = v^2 * cos40sin40
v=4.68m/s

I tried that answer, but it isn;t correct. What am i doing wrong?

 

[willem2]

This is not the same problem as a projectile problem with a 40 degree launch angle.
The horizontal speed is V_0 cos(20) and not V_0 cos (40) for example.

you need to find equations for the path of the child and for the slope and combine them
to find out where he lands

Find x, and y as a function of t for the child. (use x(t) = x_0 + v_0 t + (1/2) a t^2)

find y as a function of x for the child.

find y as a function of x for the slope.

The child will land if these functions have the same value.
you get an equation with V_0 and x in it, which you can solve for V_0