A particle is thrown with a speed of $12\, m/s$ at an angle $60^o$ with the horizontal. The time interval between the moments when its speed is $10\, m/s$ is $(g = 10\, m/s^2)$.........$s$

The angle of projection at which the horizontal range and maximum height of projectile are equal is

A particle of mass $100\,g$ is projected at time $t =0$ with a speed $20\,ms ^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\,s$ is found to be $\sqrt{ K }\,kg\,m ^2 / s$. The value of $K$ is $............$ $\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$

A body is thrown at angle $30^{\circ}$ to the horizontal with the velocity of $30\; m / s$. After $1\;sec$, its velocity will be (in $m/s$) $\left(g=10\; m / s ^{2}\right)$

Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$ : When a body is projected at an angle $45^{\circ}$, it's range is maximum.

Reason $R$ : For maximum range, the value of $\sin 2 \theta$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below :

A particle is thrown with a velocity of $u \,m / s$. It passes $A$ and $B$ as shown in figure at time $t_1=1 \,s$ and $t_2=3 \,s$. The value of $u$ is ....... $m / s$ $\left(g=10 \,m / s ^2\right)$