A projectile launched at 100 m/s and at an angle of 30°. Find the magnitude of the velocity at t = 8 seconds.

(attachment 1)

Could someone explain to me why the **second method** is **working**?

For v^{2} = u^{2} + 2as,

The velocity used is the **overall velocity** (100m/s), but the acceleration and displacement (a_{y} and s_{y}) are from the **vertical component.**

Many sources even emphasise the subscripts in the formula (attachment 2).

Oddly enough, this works for all values of time (or any other variable).

Thank you.

The reason for this is because in Physics we usually say the Horizontal velocity is constant. Which means the only acceleration the projectile experiences is in the y direction. I'll prove it to you

Start off with:

Since the acceleration in 'x' is always zero the 2a(Delta x) term is completely missing. This means we don't even need to consider the displacement in the x direction!

The formula you gave in the second image is

**ONLY** for the velocity in the Y direction. Whereas the one without the subscripts is for

**TOTAL** velocity, hopefully you can see why it works in my working out. Both formulas are correct but calculate different velocities.

Good question, hopefully this solidifies your understanding =)