Particle is dropped from the height of  $20\,\,m$ on horizontal ground. There is wind blowing due to which horizontal acceleration of the particle becomes  $6\,\,ms^{-2}$ . Find the horizontal displacement of the particle till it reaches ground.......$m$

A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $0.5 s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 m / s ^2$.

($1$) The value of $t$ is. . . . . . 

($2$) The value of $x$ is. . . . . 

Give the answer or qution ($1$) and ($2$)

A bomber plane moves horizontally with a speed of $500\,m/s$ and a bomb released from it, strikes the ground in $10\,sec$. Angle with horizontal at which it strikes the ground will be $(g = 10\,m/s^2)$

In the figure shown, velocity of the particle at $P \,(g = 10\,m/s^2)$

Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buldings $100 \;\mathrm{m}$ apart and of same helght of $200 \;\mathrm{m}$ with the same velocity of $25\; \mathrm{m} / \mathrm{s}$. When and where will the two bullets collide. $\left(g=10 \;\mathrm{m} / \mathrm{s}^{2}\right)$

Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity $g$ is uniform. If $u_1$ and $u_2$ be their initial speeds, then the time $t$ after which their velocities are mutually perpendicular is given by