Question

You walk 4.5 km in one direction then make a 45 degree turn to the right and walk another 6.4 km what is the magnitude of your displacement

Answer 1

The magnitude of your displacement is 4.52 Km

Step-by-step explanation:

Initially you walk 4.5 km in one direction. Then after turning to 45 degrees then you walk 6.4 km

So let us use cosine formula to find the distance

Distance =
`\sqrt{a^2 +b^2 -2abcos(angle)`

Substituting the given values

Distance =
`√(4.5^2 +6.4^2 -2(4.5)(6.4)cos(45))`

Distance =
`√(20.25+40.96 -2(4.5)(6.4)(0.707))`

Distance =
`√(20.25+40.96 -2(28.8)(0.707))`

Distance =
`√(20.25+40.96 - (57.6)(0.707))`

Distance =
`√(20.25+40.96 - 40.72)`

Distance = 4.52 km