Solution to a projectile problem

From J3 Physics

Here's the problem (a revised version of the problem on the board): A projectile is launched at 50 m/s at an angle of 36.87° toward a 20-meter high cliff 120 meters away. The top of the cliff is a very long plateau. Where does the projectile land (from in-class discussions we know it hits on top of the plateau somewhere).

Catherine's solution:

Resolve the initial velocity into components:

v_0x = v₀ cos(36.87) = 50(.8) = 40 m/s

v_0y = v₀ sin(36.87) = 50(.6) = 30 m/s

In the y direction, we know:

s = 20 m, v₀ = 30 m/s, a = -10m/s²

We could solve for t using a quadratic, but let's avoid that and solve for v_f:

y: v_f² = v₀² + 2as

y: v_f² = (30)² + (2)(-10)(20)

y: v_f = -22.4 m/s (We use the negative square root used because projectile is falling)

Now,

v_f = v₀ + at

t = (-22.4-30)/-10 = 5.24 sec

This allows us to solve easily for s_x:

x: s = v_avgt = (40)(5.24) = 209.6 meters