Relativity, black holes and quantum mechanics

There are 3 NRICH Mathematical resources connected to Relativity, black holes and quantum mechanics
Escape from planet Earth
problem

Escape from planet earth

Age
16 to 18
Challenge level
filled star filled star empty star
How fast would you have to throw a ball upwards so that it would never land?
The ultra particle
problem

The ultra particle

Age
16 to 18
Challenge level
filled star empty star empty star
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991