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:
- Identify the target variable and known variables for each direction—remember that only 3 of the 5 variables (Δx or Δy, v0, vf, a, and t) are needed for each direction. Also, it always helps to sketch out the problem and label all your known information!
- Choose a UAM equation—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.
- Solve the equation for the target (or intermediate) variable, then substitute known values and calculate the answer.
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: