How to find the initial velocity from this setup?

Question

Hello I'm given an assignment to build a homemade catapult which I already have, and I'm required to determine the initial velocity of a projectile.

To do this, I'm told to place my phone and ensure that it is facing the side of the catapult directly. I have to record the catapult in slow motion and determine its initial velocity from two consecutive images of the projectile position as it leaves the catapult. It's found by measuring the distance of the projectile and the time interval between the consecutive images but I'm still confused as to do.

Can someone please help me? What must I do, and what relevant formulas must I apply here?

Answer 1

It sounds like you just use the definition velocity = displacement / time interval, so v = (s₂ - s₁)/Δt. This will give the average velocity over the time interval; if the interval is very short, then the result is an approximate value for the initial velocity.

Probably there are both horizontal and vertical components of the initial velocity. If you can measure the true distance Δs = s₂ - s₁ between the position of a point on the phone in frame 2 vs frame 1, then you have the displacement. If you need to measure x and y positions of the point separately in a normal coordinate system with x and y axes perpendicular to each other, then use the distance formula s² = x² + y² for each frame.