For a projectile motion, the angle between the velocity and acceleration is minimum and acute at

A particle starts from the origin at $$t=0$$ with a velocity of $$10 \hat{\mathbf{j}} \mathrm{ms}^{-1}$$ and move in the $$x$$-$$y$$ plane with a constant acceleration of $$(8 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-2}$$. At an instant when the $$x$$-coordinate of the particle is $$16 \mathrm{~m}, y$$-coordinate of the particle is

At a metro station, a girl walks up a stationary escalator in $$20 \mathrm{~s}$$. If she remains stationary on the escalator, then the escalator take her up in $$30 \mathrm{~s}$$. The time taken by her to walk up on the moving escalator will be

Rain is falling vertically with a speed of $$12 \mathrm{~ms}^{-1}$$. A woman rides a bicycles with a speed of $$12 \mathrm{~ms}^{-1}$$ in east to west direction. What is the direction in which she should hold her umbrella?