Vertical Component
By splitting the vector into two components, many things can be determined such as max height, time taken to reach max height, total time to reach the target and total horizontal displacement.
Observe the diagram of the vertical component on the left. To find the time taken to reach max height and what the max height is, all that is needed is the initial velocity. Acceleration is known (gravity= -9.8m/s/s) and the instantaneous speed at max height is also known (vertically motionless=0m/s).
Observe the diagram of the vertical component on the left. To find the time taken to reach max height and what the max height is, all that is needed is the initial velocity. Acceleration is known (gravity= -9.8m/s/s) and the instantaneous speed at max height is also known (vertically motionless=0m/s).
Result
Now let's assume the ball is thrown and caught at hip level (1m). Using the calculations that have been made in the previous section, absolutely everything can be found. Displayed to the left is the data when the ball is thrown, at the max and when it is caught.
- Vv = Vertical Velocity
- Vh = Horizontal Velocity
- a = Acceleration
- dv = Vertical Displacement
- dh = Horizontal Displacement
- t = Time
Because horizontal velocity does not change, max speed only depends on the change in vertical velocity. Therefore the max speeds in this scenario are instantaneously as the ball is thrown and instantaneously as it is caught: Vmax=Vr1=Vr3= 20m/s. It's max speed would be greater if it weren't caught at 1m, but allowed to continue and hit the ground. That would allow the vertical velocity to increase, and thus increase its max speed!