An astronaut orbiting the earth is preparing to dock with a westar vi satellite. the satellite is in a circular orbit 500 km above the earth's surface, where the free-fall acceleration is 8.25 m/s2. take the radius of the earth as 6400 km. determine the speed of the satellite.

As the satellite is in free fall, therefore we use the formula

Here, v is the orbital speed, r is radius of Earth plus satellite is in a circular orbit 500 km above the earth's surface and g is the satellite free-fall acceleration    .

Given   and

Substituting these values in above equation we get,

Thus, the speed of satellite in  order to maintain the  orbit is

firearm identification is the process of analyzing the bullets and cartridge cases left at a crime scene to determine if they came from a particular firearm. marks on the bullets and cartridges may be common to every firearm of that type. these are called class characteristics.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west