What is the resultant velocity obtained by adding two velocities of 5 m/s, inclined at 60 degrees to each other?
I'm sure you mean the net velocity of an object has two components that are at an angle of 60 degrees to each other and have a magnitude of 5 m/s. We have to determine the magnitude of the net velocity.
The angle between the two components is 60 degrees. The magnitude of the resultant velocity is derived by first calculating the sum of the components of the two velocities in the same direction. This is equal to 5 + 5*cos 60
=> 5 + 5/2
=> 7.5 m/s
To this we add the normal component that is equal to 5*sin 60 = 5*(sqrt 3)/2
The resultant of 7.5 and 5*(sqrt 3)/2
=> sqrt (75)
The magnitude of the resultant velocity is sqrt 75 m/s.
The magnitude of the resultant velocity is given by the formula:
v = sqrt[a^2 + b^2 + 2a*b*cos(a,b)]
Let the velocities be: a = b = 5
|v| = sqrt(5^2 + 5^2 + 2*5*5*cos60)
Since cos 60 = 1/2
|v| = sqrt(25+25+25)
|v| = sqrt 75
|v| = 5*sqrt 3
The magnitude of the resultant velocity is |v| = 5sqrt3.