Unit 1 Our Dynamic Universe Vectors - Revision CfE Higher Physics Unit 1 Our Dynamic Universe Vectors - Revision

Learning Intentions Can I calculate the equivalent vector by scale diagram or otherwise for vectors in a non-right angled triangle?

Vectors Vector quantities have both a magnitude and direction. e.g. 12 mph North 25N at 45° to the horizontal Velocity and displacement are vector quantities. velocity = displacement time  

Scalars Scalar quantities have a magnitude only. e.g. 120 kg 45 s Speed and distance are scalar quantities. speed = distance time  

Vector or Scalar ? Which of the following quantities are vectors and which are scalars? velocity energy power weight acceleration force time temperature displacement work done mass distance speed frequency

Vector or Scalar ? Vectors Scalars displacement distance velocity speed acceleration time mass force temperature weight energy work done power frequency

Adding Vector Quantities Vector quantities should be added “nose to tail”. 30N 40N resultant 40 N 30 N Use either scale drawing or trigonometry to find the magnitude and direction of the resultant. magnitude = √(a2+ b2) direction, θ = tan-1(a/b) a b θ

e.g. horizontal and vertical or North-South and East-West Vector Components Any vectors can be replaced by two other vectors at the same point acting at right angles to one another. e.g. horizontal and vertical or North-South and East-West 70 N 60° 70N 60° 70sin60° 70cos60° Use either scale drawing or trigonometry to find the magnitude of the components.

Worked Example A yacht sails 4 km North, 6 km East and finally 1 km South. Calculate the final displacement of the yacht. magnitude = √(a2+ b2) 6 km = √(62+ 32) 1 km 4 km = 6.71 km resultant q direction, θ = tan-1(a/b) = tan-1(6/3) = 63.4° displacement = 6.71 km at 063°