Question

A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 146 cm and makes an angle of 124° with the positive x axis. The resultant displacement has a magnitude of 137 cm and is directed at an angle of 32.0° to the positive x axis. Find the magnitude and direction of the second displacement.

Answer 1

Answer:

B = 191.26 cm

θ = -14.73°

Explanation:

given,

magnitude of the first displacement(A) = 146 cm

at an angle of 124°

resultant magnitude = 137 cm

and angle made with x-axis by the resultant(R) = 32.0°

component of A in X and Y direction

A x = A cos θ  = 146 cos 120° = -73 cm

A y = A sin θ = 146 sin 120° = 126.4 cm

now component of resultant in x and y direction

R x = 137 cos 35°

    = 112.2 cm

R y = 137 sin 35°

     = 78.6 cm

resultant is the sum of two vectors

R = A + B

R x = A x + B x

B x =  112.2 - (-73) = 185.2 cm

B y = R y - A y

B y = 78.6 - 126.4 = -47.8 cm

magnitude of B

B = $\sqrt{B_x^2+B_y^2}$

B = $\sqrt{185.2^2+-47.8^2}$

B = 191.26 cm

angle$\theta = tan^{-1}\dfrac{-47.8}{185.2}$

θ = -14.73°