Question

find the resolved part of a force equal to 60 kg wt. in a direction making angle equal to tan-1 3/4 with its direction .​

Answer 1

Answer:

Let P be horizontal in the direction of unit vector i.

The resultant is also P but perpendicular to it in the direction of unit vector j.

If Q be the other force making an angle θ (obtuse) as resultant is perpendicular to P,

then the two forces are Pi and cosθi+Qsinθj.

Their resultant is Pj.

∴Pj=Pi+(Qcosθi+Qsinθj)

Equating the coefficients of i and j, we get P+Qcosθ=0 and P+Qsinθ=P.

or Qcosθ=−P and Qsinθ=P

Squaring and adding Q=P

2

Answer 2

Answer:

Answer:

Let P be horizontal in the direction of unit vector i.

The resultant is also P but perpendicular to it in the direction of unit vector j.

If Q be the other force making an angle θ (obtuse) as resultant is perpendicular to P,

then the two forces are Pi and cosθi+Qsinθj.

Their resultant is Pj.

∴Pj=Pi+(Qcosθi+Qsinθj)

Equating the coefficients of i and j, we get P+Qcosθ=0 and P+Qsinθ=P.

or Qcosθ=−P and Qsinθ=P

Squaring and adding Q=P

2