## Kinematics Examples

Symmetry in Kinematics Problems

For those in Sec 3 studying Kinematics now and for those in Sec 4 taking the O-Level this year, remember a couple of quick points about the symmetry of kinematics problems:

1. If you throw a ball up in the air vertically with a speed of 10 m/s, it will come back down with the same speed in the opposite direction.

2. If you throw a ball up in the air and it takes 2 seconds to reach the highest point, then it takes 2 seconds from the highest point to fall back to the ground.

This all assumes no air friction. With air friction the returning speed is slower.

See if you can also follow these two examples:

1. A ball thrown vertically down toward the ground from a 50 meter tall building with an initial speed of 20 m/s. Assuming that it falls without air friction, what is the velocity when it hits the ground?

It should make sense that we now have a faster velocity since we threw the ball downward to begin with.

2. A ball is thrown directly upward from a 50 meter tall building with an initial speed of 20 m/s. Assuming that it falls without air friction, what is the velocity when it hits the ground?

We took the initial velocity here as a negative number because the ball was thrown upward and we are calling downward positive. If a ball is thrown up at 20 m/s by the time it gets back down to the top of the roof, it is going downward at 20 m/s. So the answer comes out to the same number!