A rocket moves with initial velocity v0 towards the Moon of mass M, radius r0. Find the cross section σ for striking the Moon, taking the Moon to be at rest and neglecting all other bodies. Hint: σ is the area of the cross section of the cylinder of initially parallel orbits far from the Moon that eventually strike it. The enhancement of this cross section over the pure geometrical cross section πr02 is known as gravitational focusing.

We all use gps today, even if we don't drive yet. i bet you have been in the car with a parent and they have asked you to get out your phone to find a specific location. in your car, on the phone, you are using a very sophisticated technology. gps satellites circle the earth twice a day in a very precise orbit and transmit signal information to earth. gps receivers take this information and use trilateration to calculate the user's exact location. essentially, the gps receiver compares the time a signal was transmitted by a satellite with the time it was received. the time difference tells the gps receiver how far away the satellite is. now, with distance measurements from a few more satellites, the receiver can determine the user's position and display it on the unit's electronic map. what type of signal is utilized by the gps satellite?

Assume similar data for the motion of the blood in your aorta. estimate how many beats of the heart it will take the blood to get from your heart to your brain. (assume that the distance from your heart to your brain is 30 cm)

The slope of a velocity time graph over any interval of time gives the during that interval