A bus starts off with a speed of 20 m/s. It is moving in a direction that is 41 degrees from due east (positive numbers being counter-clockwise). After 20 seconds the bus' speed is 45 m/s and it is now moving in a direction that is 56 degrees from due east. What is the angle in degrees of the vector that represents the change in the velocity of the bus

( 24.19 / 10.06 )

Explanation:

starting speed = 20m/s

direction = 41 degrees from due east

after 20 seconds

bus speed = 45m/s

direction = 56 degrees from due east

calculate the angle of the vector that represents the change in the velocity of the bus

change in velocity : ΔV = Vf - Vi

Vf = Vf ( cos βi + sinβj )

   = 45m/s ( cos 56 i + sin56 j )

   = 25.16 i  +  37.31 j

Vi = Vi ( cos ∝ i + sin ∝ j )

   = 20 m/s ( cos 41 i  + sin 41 i )

   = 15.10 i   +  13.12j

Hence the change in velocity ΔV (  Vf - Vi )

=  10.06 i  +  24.19 j

the angle in degrees ( ∅ ) = ( 24.19 / 10.06 )

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hope this !