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
$\frac{\sqrt{u_1 u_2}}{g}$
$\frac{\sqrt{u_1^2+u_2^2}}{g}$
$\frac{\sqrt{u_1\left(u_1+u_2\right)}}{g}$
$\frac{\sqrt{u_2\left(u_1+u_2\right)}}{g}$
A train is moving along a straight line with a constant acceleration ' $a$ '. A boy standing in the train throws a ball forward with a speed of $10 \ m / s$, at an angle of $60^{\circ}$ to the horizontal. The boy has to move forward by $1.15 \ m$ inside the train to catch the ball back at the initial height. The acceleration of the train, in $m / s ^2$, is
Two paper screens $A$ and $B$ are separated by distance $100 \,m$. A bullet penetrates $A$ and $B$, at points $P$ and $Q$ respectively, where $Q$ is $10 \,cm$ below $P$. If bullet is travelling horizontally at the time of hitting $A$, the velocity of bullet at $A$ is nearly .......... $m / s$
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 body is thrown horizontally from the top of a tower of height $5 \,m$. It touches the ground at a distance of $10 \,m$ from the foot of the tower. The initial velocity of the body is ......... $ms^{-1}$ ($g = 10\, ms^{-2}$)
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 ........ $^o$