Question

A runner first runs a displacement A of 3.20 km due south, and then a second displacement B that points due east. (a) The magnitude of the resultant displacement A + B is 5.38 km. What is the magnitude (in m) of B?

Answer 1

Answer:

B = 4325 m

Explanation:

Resolving the displacement into x and y components.

Let north = positive y component

East = positive x component

So,

Rx = B

Ry = -3.20 km

Magnitude of the resultant displacement is

R = √(B^2 + (-3.20)^2)

R is given as R = 5.38 km

Making B the subject of formula;

B = √(R^2 - (-3.20)^2)

B = √(5.38^2 - (-3.20)^2)

B = 4.325 km

B = 4325 m

Answer 2

Answer: 4,438.96m

Explanation:

(kindly find attachment below)

From the attachment below, it can be seen that the resultant displacement and the other 2 displacements form a right angle triangle, with A+B as the hypotenus, 3.2km as the opposite and the displacement B as the adjacent.

By using phythagoras theorem

H² = O² + A²

(5.38)² = (3.20)² + B²

28.944 = 10.24 + B²

B² = 28.944 - 10.24

B² = 18.7044

B = √18.7044

B = 4.439km to meter is 4.439 * 1000 = 4,438. 96m