A boat crosses a river from part $$A$$ to part $$B$$, which are just on the opposite side. The speed of the water. $$v_\omega$$ and the of boat is $$v_B$$ relative to still water. Assume $$v_B=\sqrt{2} v_\omega$$. What is the time taken by the boat, if it has to cross the river directly on the $$A B$$ line ($$D=$$ width of the river) ?

A projectile is projected with the velocity of $$(3\widehat i + 4\widehat j)$$ m/s. The horizontal range of the projectile will be

A man walks in a straight line for 5 min with a velocity of 45 m/s. What is the speed with which he has to move in order to comeback to its original position in 1.5 min?

A projectile is given an initial velocity of $$(\widehat i + \widehat j)$$ m/s, where, $$\widehat i$$ is along the ground and $$\widehat j$$ is along the vertical. If g = 10 m/s^{2}, then the equation of its trajectory is