Question

the first displacement is 7 m and the second displacement is 3 m. They cannot add together to give a total displacement of:

a. 4 m

b. 10 m

c. 7 m

d. 3 m

Answer 1

Ans- (d)- They not add together to give total displacement 3m.

Resultant displacement

$For \ \ displacement \ \ vector \ \ S_{1} \ \ and \ \ S_{2} \ \ with \ \ an \ \ angle \ \ \theta \\ \ \ \\ \ \ \ \ \ \ S= \sqrt ( S_{1}^{2}+S_{2}^{2}+2 S_{1}S_{2} \ \ cos \theta) \\ \ \ Minimum \ \ displacement \ \ when$

$cos \theta = -1, S= \sqrt ( S_{1}^{2}+S_{2}^{2}-2 S_{1}S_{2}) \\ => S= \sqrt (S_{1}-S_{2})^{2} \\ => S= \left | (S_{1}-S_{2}) \right | \\ And \\ For \ \ maximum \ \ displacement \ \ cos\theta = 1 \\ S= \sqrt ( S_{1}^{2}+S_{2}^{2}+2 S_{1}S_{2}) \\ => S= \sqrt (S_{1}+S_{2})^{2} \\ => S= \left | (S_{1}+S_{2}) \right | \\ Hence$

Resultant displacement will be from 4m to 10m.

Hence it will be 4 when both are opposite vector 7-3.

And it will be 10 when both are in same direction.