Question

During an off-day, Mike Trout, Shohei Ohtani, and Albert Pujols and having a pool party. They are tugging on a ring for some odd reason (The Angels are weird…). Trout pulls with a force of 150 N directly north, Ohtani pulls directly east with a force of 100 N, and Pujols pulls southwest (225° clockwise from north) with a force of 200 N. What is the resultant force and what is the direction of the resultant force?

Answer 1

Answer:

$\left \| F \right \| = 42.3 N$

$\theta = 11.7$ degree north of west

Explanation:

Given data:

Force by trout 150 N

Force by Ohtani 100 N

Force by pujols 200 N

Net force is given as

$F = 150 j - 200\times cos 45j + ( 100i - 200\times sin45 i)$

$F = (100 - 100\sqrt {2}) i + (150 - 100\sqrt{2}) j$

$\left \| F \right \| = \sqrt{(100 - 100\sqrt{2})^2 + (150 -100\sqrt{2})^2}$

$\left \| F \right \| = 42.3 N$

Direction is

$tan\theta = \left | \frac{150-100\sqrt{2}}{100-100\sqrt{2}} \right |$

$\theta = 11.7$ degree north of west