Friction-less speed physics problem

[tthaitanium]

i have a question about this problem:

a frictionless curve of radius 100 meters, banked at an angle of 45 degrees may be safely negotiated at a speed of?

 

[HallsofIvy]

FRICTIONLESS? Ouch! Calculate the accelaration vector of an object moving around the curve at speed "v". For what speed is this vector at 45 degrees to the vertical?

 

[tthaitanium]

how would i do that?

 

[tthaitanium]

also, there's another question i have..

the tiny planet mercury has a radius of 2400 kilometers and a mass of 2.2 x 10^23 kilograms. what would be the gravitational acceleration of an astronaut standing on the surface of mercury?

can someone help me take this step by step..i have no clue how to do this

 

[prasanna]

Since the astrinaut is standing on the surface, the acceleration is zero!

But if you meant the acceleration due to gravity,g, at the surface, there is a simple formula

Loads of gravitation formula are available on the thread 'Formulas'
started by truimphdog1 on 7 or 8 or 9 December (whichever date according to your time zone)

The formula required for this question is available there

try searching and tell me if you get it!

 

[$id]

i have a question about this problem:

a frictionless curve of radius 100 meters, banked at an angle of 45 degrees may be safely negotiated at a speed of?

The formula for the centripetal acceleration is v^2/R incase you didn't know