What is the distance travelled by a point during the time \(\tau\).If, it moves in X-Y plane according to the relation, \(x=a\sin\omega.t\), \(y=a\left(1-\cos\omega.t\right)\)?
Ans: \(V=a\omega\).
A particle starts from the origin at t=0 with a velocity of \(50\hat{i}\) \(ms^{-1}\) and moves in X-Y plane under action of a force which produces a constant acceleration of \(\left(3.0\hat{i}+2.0\hat{j}\right)ms^{-1}\). (a) What is the Y-Coordinate of the particle at the instant its X-coordinate is 84m?(b) What is the speed of the particle at this time?
Ans:(a) \(Y=36m\) (b) \(v=25.94\frac{m}{s}\).
A vector \(\vec{A}\) having magnitude A is turned through an angle \(\theta\).Calculate the change in the magnitude of vector \(\vec{A}\).
Four persons A,B,C and D are initially at rest at the four corners of a square of side a. Each person is now moving with uniform speed v in such a way that A always moves directly towards B, B directly towards C, C directly towards D and D directly towards A. Show that the four person meet at a time \(t=\frac{a}{v}\).
Ans: \(t=\frac{a}{v}\).
Two vectors \(\vec{P}\) and \(\vec{Q}\) acts at a point and have a resultant \(\vec{R_{1}}\). If, \(\vec{Q}\) is replaced by the vector \(\vec{\frac{\left(R_{1}^{2}-P^{2}\right)}{Q}}\), acting in opposite direction of the \(\vec{Q}\). Show that the resultant still of magnitude \(R_{1}\).
Two cars starts together from the same point and move along two straight lines inclined at an angle \(\theta\), one moving with a velocity u and the other from rest with uniform acceleration a. Show, that the least relative velocity between them is \(u\sin\theta\) and occures after time, \(t=\frac{u\cos\theta}{a}\).
