Projectile Motion velocity and direction

[aaronfue]

Homework Statement

At t = 0, a projectile is located at the origin and has a velocity of 20 m/s at 40° above the horizontal. The profile of the ground surface it strikes can be approximated by the equation y = 0.4x – 0.006x², where x and y are in meters. Determine (a) the approximate coordinates of the point where it hits the ground, (b) its velocity and direction when it hits the ground, (c) its highest point in flight and (d) the greatest distance above the ground.

Homework Equations

v_o= 20 $\frac{m}{s}$
θ=40°
Horizontal Motion: x=x_o² + (v_o)_x²t + $\frac{1}{2}$at
Vertical Motion: y=y_o² + (v_o)_y²t + $\frac{1}{2}$at

The Attempt at a Solution

This function of the ground is confusing me. I'm not sure where to start with this.

 

[tms]

When you do one of these problems with a flat ground you also have do deal with a function that describes the height of the ground at a given distance, but it is easy since the function is constant. Here you do the same thing, but you have a non-constant function for the ground. In both cases you find the place where the trajectory intersects the ground.

 

[haruspex]

Horizontal Motion: x=x_o² + (v_o)_x²t + $\frac{1}{2}$at
Vertical Motion: y=y_o² + (v_o)_y²t + $\frac{1}{2}$at

The powers of 2 are in the wrong places.

 

[aaronfue]

The powers of 2 are in the wrong places.

Got it. Thanks!