Question

The magnitude and direction exerted by two tugboats towing a ship are 1670 ​kilograms, N30degrees​W, and 1250 ​kilograms, S60degrees​W, respectively. Find the​ magnitude, in​ kilograms, and the direction​ angle, in​ degrees, of the resultant force.

Answer 1

Answer:

magnitude=2085.99 kg

direction angle= 23.18°

Explanation:

let the forces be x,y

x = 1670cos(90°+30°) i +1670sin(90°+30°) j,

y = 1250cos(-90°-60°) i +1250sin(-90°-60°) j

x = 1670cos(120°) i +  1670sin(120°) j,

y = 1250cos(-150°) i + 1250sin(-150°) j

resultant force = x+y

resultant force = 1670cos(120°) i +1670sin(120°) j + 1250cos(-150°) i +1250sin(-150°) j

taking i and j term together

resultant force = (1670cos(120°) +1250cos(-150°)) i +(1670sin(120°) +1250sin(-150°)) j

resultant force = -1917.53 i +821.26j

$magnitude=\sqrt {(-1917.532)^{2} + (821.26)^{2}}$

magnitude=2085.99 kg

direction angle= $tan^{-1}(\frac{821.26}{1917.53})$

direction angle= 23.18°