Question

a ship leaves a port P and travels 30 km due north . then it changes course and travels 20 km in a direction 30° east of north to reach port R. calculate the distance from P to R.

Answer 1

The distance between P and R is equal to the net displacement of the ship in going from port P to port R

Vector P = 30 km North

Vector R = 20 km 30° east of north

Now, the angle between Vector P and vector R = 90° + 30 ° = 120°

Using the formula to find the addition of two vectors:

Resultant = $= \sqrt{P^2+R^2 +2PR Cos 120}$

Plugging the values:

$Resultant = \sqrt{30^2+20^2+2\times 20 \times 30 \times (-0.5)}$

$Resultant = \sqrt{900 +400 -600 }$

Resultant = 26.457 Km

The distance from P to R is 26.457 km