Answer to Question 1
Examining the different seismic waves we find P and S waves are not recorded by all over the planet. There is a blind spot for S waves on the side of Earth opposite the earthquake, and there is a shadow zone part way around the surface from the earthquake. Since we know S waves cannot travel through liquid and P waves can, we conclude the Earth's core is liquid. Since P waves bend when they enter the liquid core, but some travel straight through, it implies there is a solid center to the liquid outer core.
Answer to Question 2
The Doppler gun can focus on the motion of the baseball, and give us the speed that the pitcher is delivering it to the plate.