If I have a ball thrown horizontally with a speed u off a building of height h , how do I calculate its speed when it hits the ground?

Here we will want to use the SUVAT equations, which I'm sure you will have come across. Notice that in the question we only have an initial horizontal velocity and because we model all objects as points, we assume that no force acts on the ball to change the horizontal element of its speed. Now we consider the vertical direction separately. Remember, we want to find the ball's velocity when it hits the ground. Let's think about which out of the variables SUVAT we have.s = displacement = h = height of the building u = initial velocity = 0 because at the start the ball is not moving up or downv = final velocity this is what we want to finda = g = force due to gravity sometimes we approximate this to a number but let's stick with g for nowt = time taken we have no information about this. I remember that an equation linking s, u, v and a is: v² = u² + 2asLet's use that now: v² = 0² + 2gh, so v² = 2gh, so v = square root of 2gh. to find the ball's speed when it hits the ground we must combine the horizontal and vertical components using Pythagoras' Theorem: speed² = u² + 2gh, so our final answer is speed = sqrt(u² + 2gh) where we can input values for u, g and h.