🤓 Based on our data, we think this question is relevant for Professor Hatch's class at UMASS.
A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at 43.0 above the horizontal toward the cliff.
What must the minimum muzzle velocity be for the shell to hit the top edge of the cliff?
This problem is asking us to find the minimum initial velocity of a projectile given the direction of the initial velocity and the horizontal and vertical distance it has to travel.
For projectile motion problems in general, we'll follow these steps to solve:
The four UAM (kinematics) equations are:
We define our coordinate system so that the +y-axis is pointing upwards and the +x-direction is horizontal along the launch direction. That means ay = −g, and ax = 0 (because the only acceleration acting on a projectile once it's launched is gravity.)
For projectiles with a positive launch angle, we also need to know how to decompose a velocity vector into its x- and y-components: