Standard content

A ball thrown up a hill lands somewhere new, and a ball thrown from a moving lorry follows two paths at once. Here you handle throws on slopes and from moving platforms, and you find the farthest point that any throw can reach. You follow two ships to see how close they come, and you describe a car that speeds up on a bend. The problems are at the level of JEE, A-Level Physics and IB Higher Level, with a long timed paper.

What's inside

1. Slopes, moving platforms and the farthest reach: A ball thrown up a hill, a ball thrown from a moving lorry, and the farthest point that a throw can reach. Tilted axes make the hill simple, a change of frame makes the lorry simple, and the envelope of all the paths shows the limit.
2. Closest approach, interception and fast rivers: Two bodies on straight courses can pass close or collide, and the answer sits in their relative velocity. This lesson finds the closest approach, aims a pursuer at a moving target, steers a boat that is slower than the river, and reads rain from two moving observers.
3. Circular motion with changing speed: A car on a bend that speeds up has two accelerations at right angles. One changes the speed and the other changes the direction. The same split works for any curved path, and it gives the radius of curvature at every point.