Two forces whose magnitude are in ratio \(\frac{3}{5}\) give a resultant of 28N. If, the angle of inclination is \(60^{o}\). Find the magnitude of each force?
Ans: \(F_{1}=12N\) and \(F_{2}=20N\).
A motor boat is racing towards north at \(25 km h^{-1}\) and the water current is in that region is \(10 km h^{-1}\) in the direction of \(60^{o}\) east of south. Find, Resultant velocity of the boat?
Ans: \(v=21.8km.h^{-1}\) and \(\alpha=23.4^{o}\).
Two vectors, both equal in magnitude have their resultant equal in magnitude with either. Find, the angel between them?
Ans: \(\theta=120^{o}\).
At what angle do the forces \(\left(P+Q\right)\) and \(\left(P-Q\right)\) acts so that resultant is \(\sqrt{3P^{2}+Q^{2}}\)?
Ans: \(\theta=60^{o}\).
The resultant of two equal forces acting at right angel to each other is \(14.14 N\). Find, the magnitude of either forces?
Ans: \(F_{1}=F_{2}=10N\).
Find, the magnitude of the resultant velocity if a body is simultaneously given two velocities, one \(30 ms^{-1}\) due east and othe \(40 ms^{-1}\) due north?
Ans: \(50\frac{m}{Sec}\).
Find the angle between two vectors \(\vec{P}\) and \(\vec{Q}\). If, the resultant of vectors is given by, \(R^{2}=P^{2}+Q^{2}\).
Ans: \(\theta=\frac{\pi}{2}\).
A ship is streaming due east at \(12 ms^{-1}\). A women runs across the deck at \(5 ms^{-1}\) in a direction at right angel to the direction of motion of the ship and then towards north. Calculate, velocity of women relative to the sea?
Ans: \(v_{R}=13\frac{m}{s}\) and \(\alpha=22^{o}\).
Two forces have a resultant equal to \(\frac{3}{2}\) times the either forces. At what angel do the forces are inclined to each other?
Ans: \(\theta=82^{o}\).
A particle has a displacement of \(12 m\) due east and \(5 m\) due north and then \(6 m\) vertically upwards. Find the magnitude of the sum of these displacement.
Ans: \(14.32m\).
A particle initially at A\(\left(2,4,6\right)\) \(m\) moves finally to the point B\(\left(3,2,-3\right)\) \(m\). write the (i) initial position vector (ii) final position vector and (iii) displacement vector of the particle.
Ans:(i) \(\vec{r}_{i}=2\hat{i}+4\hat{j}+6\hat{k}\), (ii) \(\vec{r}_{f}=3\hat{i}+2\hat{j}-3\hat{k}\) and (iii) \(\vec{\Delta r}=-\hat{i}+2\hat{j}+9\hat{k}\).
A particle has following displacement in succession: (a) 12 m towards direction X. (b) 5 m towards Y. and (c) Finally, 6 m towards direction Z. Find, the magnitude of the resultant displacement.
