Calculating sound waves, wavelength shift in regards to the Doppler Effect.

A sound detector is placed on a railway platform. A train, approaching the platform at a speed of 36km/h sounds its whistle. The detector detects 12 kHz as the most dominant frequency in the whistle. If the train stops at the platform and sounds the whistle, what would be the most dominant frequency detected? The speed of sound in air is 340m/s.

Sample problem on instantaneous velocity.

The position of a particle moving on an x axis is given by: x=7.8 + 9.2t - 2.1t^3 with x in meters and t in seconds. What is its velocity at t=3.5s? Is velocity constant or changing?

mechanics

1)a.A grind stone of 0.1m thick,1m of diameter and a relative density of 2.53 find-moment of inertia+ radius of gyration. b)A gun is fired at a target 12km away at an angle of 35deg and hits target.How long is the projectile in the air and what's it's velocity? need complete step by step answer,thanks..

Working with vector magnitude and direction.

Given 2 vectors V1=(6,8) and V2=(-11,4) find the magnitude and direction of V1 + V2 and V1 - 2V2

Working with velocity, distance and time.

It takes 4 years to reach the nearest star. The speed of light is c=3.00x10^8m/s. How many kilometers away is the star?