A projectile fired at $$30^{\circ}$$ to the ground is observed to be at same height at time $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ after projection, during its flight. The speed of projection of the projectile is ___________ $$\mathrm{m} ~\mathrm{s}^{-1}$$.
(Given $$g=10 \mathrm{~ms}^{-2}$$ )
The speed of a swimmer is $$4 \mathrm{~km} \mathrm{~h}^{-1}$$ in still water. If the swimmer makes his strokes normal to the flow of river of width $$1 \mathrm{~km}$$, he reaches a point $$750 \mathrm{~m}$$ down the stream on the opposite bank.
The speed of the river water is ___________ $$\mathrm{km} ~\mathrm{h}^{-1}$$
An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _________ degree.