Question

a body of mass 200g is initially at rest, 2 forces of 1800 dine each do simultaneously the body. if the forces make 120 degree with each other, how far does the body travel in 2 seconds?

Answer 1

Task. A body of mass 200g is initially at rest, 2 forces of 1800 N each do simultaneously the body. If the forces make 120 degree with each other, how far does the body travel in 2 seconds?

Solution. First we should compute the sum of these forces. Choose coordinates as shown in the following figure:

Then the resulting force is directed along $x$-axis and has absolute value

$F=2*1800*cos60{}^{\circ}=2*1800*\frac{1}{2}=1800N.$

By the second Newton’s law the body will move with acceleration $a$ satisfying the following relation:

$F=ma,$

whence

$a=\frac{F}{m}=\frac{1800}{200}=9m/s^{2}.$

Suppose that the body was at rest and he forces are applied at time $t=0$. Then at time $t$ the body will pass the distance

$d(t)=\frac{at^{2}}{2}.$

Substituting values we get:

$d(2)=\frac{at^{2}}{2}=\frac{9*2^{2}}{2}=18\ m$

Answer. 18 m.