Given that $u_x=$ horizontal component of initial velocity of a projectile, $u_y=$ vertical component of initial velocity, $R=$ horizontal range, $T=$ time of flight and $H=$ maximum height of projectile. Now match the following two columns.
Column $I$ | Column $II$ |
$(A)$ $u_x$ is doubled, $u_y$ is halved | $(p)$ $H$ will remain unchanged |
$(B)$ $u_y$ is doubled $u_x$ is halved | $(q)$ $R$ will remain unchanged |
$(C)$ $u_x$ and $u_y$ both are doubled | $(r)$ $R$ will become four times |
$(D)$ Only $u_y$ is doubled | $(s)$ $H$ will become four times |
$( A \rightarrow q , B \rightarrow q , r , C \rightarrow r , s , D \rightarrow s )$
$( A \rightarrow s , B \rightarrow q , r , C \rightarrow r , s , D \rightarrow p )$
$( A \rightarrow p , B \rightarrow q , r , C \rightarrow r , s , D \rightarrow s )$
$( A \rightarrow q , B \rightarrow q , p , C \rightarrow r , s , D \rightarrow s )$
A particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to $v$, where
A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is
Ratio between maximum range and square of time of flight in projectile motion is
The projectile motion of a particle of mass $5\, g$ is shown in the figure.
The initial velocity of the particle is $5 \sqrt{2}\, ms ^{-1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 10^{-2}\, kgms ^{-1} .$ The value of $x ,$ to the nearest integer, is ...... .
A projectile crosses two walls of equal height $H$ symmetrically as shown The time of flight $T$ is given by ........ $\sec$