A body of mass $2\; kg$ has an initial velocity of $3 \;m / s$ along $OE$ and it is subjected to a force of $4$ newtons in $OF$ direction perpendicular to $OE$. The distance of the body from $O$ after $4 \;seconds$ will be

A ball is held in the position shown with string of length $1\,\, m$ just taut & then projected horizontally with a velocity of $3 \,\,m/s$. If the string becomes taut again when it is vertical, angle $\theta$ is given by  ........ $^o$

An aeroplane is moving with a velocity $u$. It drops a packet from a height $h$. The time $t$ taken by the packet in reaching the ground will be

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 ($2$)

Two balls of mass $M$ and $2 \,M$ are thrown horizontally with the same initial velocity $v_{0}$ from top of a tall tower and experience a drag force of $-k v(k > 0)$, where $v$ is the instantaneous velocity. then,

An aeroplane flying $490 \,m$ above ground level at $100\, m/s$, releases a block. How far on ground will it strike ......... $km$