The problem states,
Suppose you launch a projectile at an angle with speed v. Assuming that the ground is level and we can neglect air resistance, what is the magnitude of the projectile’s impact velocity with the ground.
What are the steps to finding the answer?
Ok that makes sense. Thank you
There are two ways to solve this problem: mathematically and intuitively.
Let's start with the math approach. Consider the projectile's intial velocity's horizontal and vertical components. The horizontal component of the projectile's velocity is unchanged throughout its trajectory because there is no horizontal acceleration. Finding the final vertical velocity requires the use of DVATs. We can use the Delta y = v_iy t + 1/2 ay t^2 to find the time the projectile is in the air. We can then use v_fy = v_iy + ay t to find the vertical impact velocity. It turns out that the final y velocity is just the opposite of the initial y velocity. Since the two components have equal magnitude, the initial and horizontal velocities also have the same magnitude. This means that answer is just v.
An easier approach is realizing that no energy is lost to air resistance, so it makes sense for the impact velocity to also be v.