# Projectile Motion Lesson 3 - Bi-Level Projectile Motion

The third type of projecitle motion, which I call bi-level projectile motion, is basically like the angled projectile motion, except that the object does not land at the exact same vertical level at which it took off, it could land either higher or lower. There is really nothing new to learn, this lesson will just show you how to apply the formulas and concepts you already know to this type of projectile motion.

A cat is sitting on the edge of a 1.5m high table and jumps at a 37° angle with a speed of 10m/s. How far horizontally from the edge of the table does the cat land?

First, we are going to find the x and y components of the velocity, but instead of using the acceleration formula to find the time, since we don't know the final velocity, we must use the to find it. That also means we must use the quadratic formula.

10m/s cos 37° = 7.986m/s
10m/s sin 37° = 6.018m/s
-1.5m = 6.018m/s * t + 0.5 * -9.8m/s2 * t2
0 = -4.9m/s2 * t2 + 6.018m/s * t + 1.5m

Notice how -1.5m was put in for the distance in the equation. The reason for this is the main difference between bi-level projectile motion and angled projectile motion. Unlike angled projectile motion, where the vertical placement of the object was the same before and after, in this type of projectile motion the vertical distance is changed. In the instance of the cat, since it is sitting on a table 1.5m high, its final destination will be 1.5m below the original, hence the -1.5m distance.

In the case where an object lands on a ledge above it's current position a positive number could be substituted for distance. Remember though, the quadratic will give you two answers, representing both times the object is at that height.

Just make sure you choose the correct of the two answers. Now on to the quadratic.

0 = -4.9m/s2 * t2 + 6.018m/s * t + 1.5m
(-6.018m/s +- sqrt(36.216m2/s2 - 4(-4.9m/s2)(1.5m))) / 2(-4.9m/s2)
(-6.018m/s +- 8.100m/s) / -9.8m/s2
(-6.018m/s + 8.100m/s) / -9.8m/s2 = -0.212s
(-6.018m/s - 8.100m/s) / -9.8m/s2 = 1.441s

Since we know time cannot be negative, we will just multiply the 1.441s times the horizontal velocity.

1.441s * 7.986m/s = 11.508m

The next group of lessons deal with rotational motion. While still in the motion category, it is a little different from what we've discussed so far.