Consider two displacements, one of magnitude 15 m and another of magnitude 20 m. what angle between the directions of this two displacements give a resultant displacement of magnitude (a) 35 m, (b) 5 m, and (c) 25 m.

a) 0°

b) 180°

c) 90°

Explanation:

Hello!

To solve this question let a be the vector whose length is 15 m and b the vector of length 20 m

So:

|a | = 15

|b | = 20

Since we are looking for the angle between the vectors we need to calculate the length of the sum of the two vectors, this is:

Now we replace the value of the lengths:

--- (1)

Now, if:

a) |a+b| = 35

First we can see that 20 + 15 = 35, so the angle must be 0, lets check this:

and :

      θ = 0

b) |a+b|=5

From eq 1 we got:

  --- (2)

  θ = π     or    θ = 180°

c) |a+b|=25

  θ = π/2     or    θ = 90°

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