A horse rider covers half the distance with $$5 \mathrm{~m} / \mathrm{s}$$ speed. The remaining part of the distance was travelled with speed $$10 \mathrm{~m} / \mathrm{s}$$ for half the time and with speed $$15 \mathrm{~m} / \mathrm{s}$$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $$\frac{x}{7} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ is ___________.

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms$$^{-2}$$.

(Given g = 10 ms$$^{-2}$$)

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.

A ball is thrown vertically upwards with a velocity of $$19.6 \mathrm{~ms}^{-1}$$ from the top of a tower. The ball strikes the ground after $$6 \mathrm{~s}$$. The height from the ground up to which the ball can rise will be $$\left(\frac{k}{5}\right) \mathrm{m}$$. The value of $$\mathrm{k}$$ is __________. (use $$\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$$)