Question

An object undergoes two successive displacements:

Answer 1

The magnitude of the net displacement is 95.3 m

Explanation:

To find the magnitude of the net displacement, we have to resolve each of the two displacements into the horizontal and vertical direction first.

1st displacement is:

$d_1=79 m$ at $16.9^{\circ}$

So its components are

$d_{1x}=(79)(cos 16.9^{\circ})=75.6 m\\d_{1y}=(79)(sin 16.9^{\circ})=23.0 m$

2nd displacement is:

$d_2=16.7 m$ at $31.1^{\circ}$

So its components are

$d_{2x}=(16.7)(cos 31.1^{\circ})=14.3 m\\d_{2y}=(16.7)(sin 31.1^{\circ})=8.6 m$

Therefore, the x- and y-components of the net displacement are:

$d_x=d_{1x}+d_{2x}=75.6+14.3=89.9 m\\d_y=d_{1y}+d_{2y}=23.0+8.6=31.6 m$

Therefore, the magnitude of the final displacement is:

$d=\sqrt{d_x^2+d_y^2}=\sqrt{(89.9)^2+(31.6)^2}=95.3 m$

Learn more about displacement:

brainly.com/question/3969582

#LearnwithBrainly