# Projectile Motion: velocity and speed

1. Aug 5, 2013

### MathHelpa

I came across this one problem that asked for speed and velocity and I was wondering what the speed is suppose to be. I read somewhere that its the magnitude to velocity. So I want to see if I am doing this right.

A ball is launched off the top of a building. The initial velocity of the ball is v₀ = (v₀,0) and the initial height is H. What is the velocity and speed at the moment it hits the ground in terms of v₀,H and g?

y = v₀yt + 1/2at2
y = 0 + 1/2at2
t = √(2h/g)

vx = v₀

vy = voy + at
vy = 0 + at
vy = g√(2h/g)

|v| = √((g√(2h/g)2 + v₀2)

θ = tan-1(g√(2h/g/v₀))

v = √(g√(2h/g)2 + v₀2)m/s tan-1(g√(g√(2h/g)/v₀) positive below x axis.

So the question is the speed suppose to be sqrt(g√(2h/g)2 + v₀2)m/s??

2. Aug 5, 2013

### Enigman

Greetings,
Yes, speed is the magnitude of velocity.
Yes the answer is correct though it can be a bit more simplfied...
A hint for any future questions you may want to ask: If you don't know how to use Latex you may want to ensure your equations are at least readable. :D
For denoting power use ^ for denoting multiplication use * and if you are squaring a term with more variables then do something like this (v*w/x)^4
Regards

3. Aug 5, 2013

### Zondrina

Here's some quick advice on how to use latex for the next time. It will allow you to make your equations clear and legible. Also, you should follow the posting format for next time.

There's two different ways you can execute latex. Inline latex and emphasized latex.

Inline latex looks like this : $v = v_0t + \frac{1}{2}at^2$

Emphasized latex takes up a whole line and looks like this : $$v = v_0t + \frac{1}{2}at^2$$

To perform inline latex in your posts, simply wrap your text in $tags like so : Code (Text):$v = v_0t + \frac{1}{2}at^2##
To perform emphasized latex, wrap your text in $$tags like so : Code (Text):$$v = v_0t + \frac{1}{2}at^2
When writing within the tags, '^' allows you to write superscripts and '_' allows you to write subscripts ( There's s lot more uses for these two symbols, but as time goes on I'm sure you will get used to it ). \frac{numerator}{denominator} allows you to write fractions too.