[Explained] The car makes a displacement of 100m towards east and then 200m towards north. What is the magnitude and direction of the resultant?

In this question, we have to find the magnitude of AC Vector

Options

• A. 223,7m, tan ^{− 1} ( 2 ) , N of E
• B. 223,7m, tan ^{− 1} ( 2 ) , E of N
• C. 300m, tan ^{− 1} ( 2 ) , N of E
• D. 100m, tan ^{− 1} ( 2 ) , N of E

Solution

Given That the car makes a displacement of 100 m towards east and then 200 m towards north. What is the magnitude and direction of the resultant?

• Basic assumptions,
  • Let D denotes the magnitude of resultant displacement AC
  • Let θ denotes the angle between the resultant displacement and the displacement of 100 m towards east.
• Hence from above data we get following relations,
  • D = √(100^2 + 200^2)
    • or D = 100*√(1 + 4) = 100*√5 = 100*2.236 = 223.6 (m) 

So answer is A . 223,7m, tan ^{− 1} ( 2 ) , N of E

• tanθ = 200/100
  • • or tanθ = 2 or θ = tan^–1 (2) = 63.43° [Ans]

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