Objects A and B are at the origin. If object A moves to #(4 ,-1 )# and object B moves to #(7 ,1 )# over #3 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
1 Answer
Explanation:
We're asked to find the relative velocity of object
I'm going to assume the speed is either constant during the displacement, or we're asked to find the relative velocity at
What we can do first is find the components of the velocity of each object:
The equation here for the relative velocity of
If you're wondering why this is the equation, picture the two velocities you're adding like fractions being multiplied, where
#vecv_(B"/"O)# is#"B"/"O"# , and#vecv_(O"/"A)# is#"O"/"A"# :The velocity we want to find (
#vecv_(B"/"A)# ), which as a fraction becomes#"B"/"A"# , is the product of the two other fractions, because the#"O"# s cross-cancel:
#"B"/"A" = "B"/(cancel("O")) xx (cancel("O"))/"A"# And so written similarly the equation is
#vecv_(B"/"A) =vec v_(B"/"O) + vecv_(O"/"A)#
Notice that we calculated earlier the velocity of
These two expressions are opposites:
And so we can rewrite the relative velocity equation as
Expressed in component form, the equations are
Plugging in our known values from earlier, we have
Thus, the relative speed of
For additional information, the angle of the relative velocity vector at
#t = 3# #"s"# is
#theta = arctan((v_(By"/"Ay))/(v_(Bx"/"Ax))) = (color(green)(0.667"m"/"s"))/(color(red)(1.00"m"/"s")) = color(purple)(33.7^"o"#