Question 36: Motion in 2D & Vectors

Question

The sum of two forces $$\overrightarrow P $$
 and $$\overrightarrow Q $$
 is $$\overrightarrow R $$
 such that $$\left| {\overrightarrow R } ight| = \left| {\overrightarrow P } ight|$$
. The angle $$	heta $$ (in degrees) that the
resultant of 2$${\overrightarrow P }$$
and $${\overrightarrow Q }$$
 will make with $${\overrightarrow Q }$$
 is , ..............

Accepted Answer

$$\overrightarrow P  + \overrightarrow Q  = \overrightarrow R $$
$$ \Rightarrow $$ P
2
+ Q
2
+ 2PQcos$$	heta $$ = R
2
= P
2
[As $$\left| {\overrightarrow R } ight| = \left| {\overrightarrow P } ight|$$]
$$ \Rightarrow $$ 2Pcos$$	heta $$ + Q = 0
tan $$\alpha $$ = $${{2P\sin 	heta } \over {Q + 2P\cos 	heta }}$$ = $$\infty $$
$$ \Rightarrow $$ $$\alpha $$ = 90
o

Motion in 2D & Vectors

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