A projectile is thrown in the upward direction making an angle of $60^o $ with the horizontal direction with a velocity of $147\ ms^{-1}$ . Then the time after which its inclination with the horizontal is $45^o $ , is    ……… $\sec$

Two particles $A$ and $B$ are projected simultaneously from a fixed point of the ground. Particle $A$ is projected on a smooth horizontal surface with speed $v$, while particle $B$ is projected in air with speed $\frac{2 v}{\sqrt{3}}$. If particle $B$ hits the particle $A$, the angle of projection of $B$ with the vertical is

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.

Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^o , 30^o , 45^o $  and $60^o $ with the horizontal respectively. The body having shortest range is

Two projectiles, one fired from surface of earth with velocity $10 \,m/s$ and other fired  from the surface of another planet with initial speed $5\, m/s$ trace identical trajectories.  The value of acceleration due to the gravity on the planet is   ……… $m/s^2$