Question

A rock is thrown off a cliff with a horizontal velocity of 18.3 m/s. Right before it hits the ground, it has a vertical velocity of -31.3 m/s. What is the magnitude of the rock's overall velocity?

Answer 1

Answer: 36.257 m/s

Explanation:

The vertical and horizontal components of a projectiles motion are completely independent of each other. The only thing they share is the amount of time in the air. Because they are independent, the acceleration of gravity cannot affect the horizontal acceleration. This means horizontal acceleration is 0. If the acceleration is 0, this means the velocity does not change horizontally. So the final velocity of the x component is equal to the initial.

Now if you actually imagine these two vectors, it forms a right triangle. So you can use the Pythagorean Theorem to find the resultant vector.

$a^2+b^2=c^2\\18.3^2+(-31.3)^2 = c^2\\c = 36.257 m/s$