A water fountain on the ground sprinkles water all around it. If, the speed of water coming out of the fountain nozzle is \(v\), then calculate the total area around the fountain that gets wet.
ANS: \(A=\frac{\pi v^{4}}{g^{2}}\)
A particle is projected over a triangle from one end of the horizontal base and grazing the vertex falls on the other end of the base. If, \(\alpha\) and \(\beta\) be the base angles and \(\theta\) the angle of projection, prove that: \(tan\theta = tan\alpha + tan\beta\).
A particle of mass \(m\) is projected with a velocity \(v\) making an angle of \(30^{o}\) with the horizontal. Calculate: the magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height.
ANS: \(L=\frac{\sqrt{3}mv^{3}}{16g}\).
A shell is fired from a gun from the bottom of a hill along a slope. The s.pe of the hill is \(\alpha= 30^{o}\) and the angle of projection with respect to horizontal is \(\beta= 60^{o}\). The initial velocity \(u=21 ms^{-1}\). Find the distance from the gun to the point at the slope of the hill the shell falls.
ANS: \(30m\).
A projectile can have the same range R for two angles of projection. If, \(t_{1}\) and \(t_{2}\) be the times of flight of flights in two cases, then: Find \(t_{1}\times t_{2}\)?
ANS: \(t_{1}\times t_{2}=\frac{2R}{g}\).
The co-ordinate of a moving particle at any time \(t\) are given by \(x=\alpha t^{2}\) and \(y=\beta t^{3}\), where \(\alpha\) and \(\beta\) are constants. What is the speed of particle at time \(t\)?
ANS: \(v=3t^{2}\sqrt{\alpha^{2}+\beta^{2}}\).
A projectile is fired at an angle \(45^{o}\) with horizontal. Find: the elevation angle of the projectile \(\left(\alpha\right)\) at the highest point as seen from the point of projection.
A ball rolls off the top of a stairway with a constant horizontal velocity \(u\). If, the steps are \(h\) metre high and \(w\) metre wide. Show that: the ball will hit the edge of the \(n^{th}\) step if \(n=\frac{2hu^{2}}{gw^{2}}\).
