How long would it take to fall through the center of the Earth?

450px-9_daughters_hole
We have a hole that leads straight through the center of the Earth. We neglect air resistance and assume that the Earth has uniform density ρ. How long would it take to fall through the center of the Earth and reach the other side of the planet?

Continue reading

A passenger is late for a train

mpzm6jA passenger is late for a train. He stood at a railway station while the accelerating train passed him car by car. The passenger noticed that the last train car passed him for 8 seconds and the previous train car for 10 seconds. How long was the passenger late for the train? You should consider that the train moved with uniform acceleration and the length of the train cars is the same.

Continue reading

What is the surface temperature of the planet?

508439main_pia00007_full
A planet of radius r and mass M has a homogeneous atmosphere (density independent of height). The atmosphere has a height h and the atmosphere’s gas has a molar mass μ.
What is the surface temperature of the planet?

Continue reading

A bomber wants to hit a target

boeing_b-52_dropping_bombsA bomber flies with a constant velocity of 50 m/s horizontally and wants to hit a target traveling 20 m/s (same direction) on a highway 1000 m below. What is the horizontal distance of the bomber from the target so that a bomb released from it will hit the target?

Continue reading

Shooting a bullet horizontally and dropping a bullet

fireddroppedbulletIf you fire a bullet horizontally and drop one from your hand at the same height and time, which will hit the ground first?

Continue reading

The stones in the container

smallStonesA vertical container (right rectangular prism) with base area measuring 0.15 m by 0.2 m is being filled with identical small stones, each with a volume of 2*10-8 m3 and a mass of 0.05*10-3 kg. Assume that the volume of the empty spaces between the stones is negligible. If the height of the stones in the container increases at the rate of 3*10-3 m/s, at what rate does the mass of the stones in the container increase?
 
Continue reading