Question

A particle undergoes two displacements. The first has a magnitude of 11 m and makes an angle of 73 ◦ with the positive x axis. The result after the two displacements is 8.7 m directed at an angle of 119◦ to the positive x axis using counterclockwise as the positive angular direction Find the angle of the second displacement (measured counterclockwise from the positive x axis). Answer in units of ◦

Answer 1

Answer:

7.97253265907 m

Explanation:

First displacement

$\Delta x=11cos 73=3.216\ m$

$\Delta y=11sin 73=10.51\ m$

Final displacement

$\Delta x=8.7cos 119=-4.21\ m$

$\Delta y=8.7sin 119=7.609\ m$

Second displacement

$\Delta x=-4.21-3.216=-7.426\ m$

$\Delta y=7.609-10.51=-2.901\ m$

The magnitude of the second displacement is

$=\sqrt{(-7.426)^2+(-2.901)^2}=7.97253265907\ m$

The second displacement is 7.97253265907 m