A ball of mass m is thrown vertically upward. Another ball of mass $$2 \mathrm{~m}$$ is thrown at an angle $$\theta$$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $$\frac{1}{x}$$. The value of x is _____________.

If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajectory is $$y=5 x(1-x)$$. The $$y$$ component vector of the initial velocity is ______________ $$\hat{j}$$. ($$\mathrm{Take}$$ $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

A particle is moving in a straight line such that its velocity is increasing at 5 ms^$$-$$1 per meter. The acceleration of the particle is _____________ ms^$$-$$2 at a point where its velocity is 20 ms^$$-$$1.

A car is moving with speed of $$150 \mathrm{~km} / \mathrm{h}$$ and after applying the break it will move $$27 \mathrm{~m}$$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___________ m distance.