The figure was extracted from an old computer game, called Bang! Bang!
In the game, two competitors control cannons A and B, firing bullets alternately with the objective of hitting the opponent's cannon; to do this, they assign estimated values for the magnitude of the initial velocity of firing ($\left|\overrightarrow{v_0}\right|$) and for the firing angle ($\theta$).
At a certain moment in a match, competitor B must fire; he knows that the bullet fired previously, $\theta = 53^{\circ}$, passed tangentially through point $\boldsymbol{P}$.
In the game, $|\vec{g}|$ equals $10 \mathrm{~m/s}^2$. Consider $\sin 53^{\circ} = 0.8$, $\cos 53^{\circ} = 0.6$ and negligible action of dissipative forces.
Based on the given distances and maintaining the last firing angle, what should be, approximately, the smallest value of $\left|\overrightarrow{v_0}\right|$ that would allow the shot fired by cannon $\mathbf{B}$ to hit cannon $\mathbf{A}$?
(A) $30 \mathrm{~m/s}$.
(B) $35 \mathrm{~m/s}$.
(C) $40 \mathrm{~m/s}$.
(D) $45 \mathrm{~m/s}$.
(E) $50 \mathrm{~m/s}$.

182. Balls A and B are at distance $d$ from each other, and are simultaneously thrown horizontally from the ground surface. Ball A is thrown with speed $30\,\dfrac{\text{m}}{\text{s}}$ in the vertical direction, and ball B is thrown with speed $V_\circ$ at an angle of $45°$ to the horizontal. If both balls collide at a point, how many meters is $d$? (Neglect air resistance, $g = 10\,\dfrac{\text{m}}{\text{s}^2}$)
$$30 \quad (1) \qquad 45 \quad (2) \qquad 60 \quad (3) \qquad 90 \quad (4)$$

A ball projected from ground at an angle of $45^{\circ}$ just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is:
(1) 4.4 m
(2) 2.4 m
(3) 3.6 m
(4) 1.6 m

The initial speed of a bullet fired from a rifle is $630 \mathrm{~m} / \mathrm{s}$. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target should the rifle be aimed so that the bullet hits the centre of the target? (Take $g = 10 \mathrm{~m/s}^2$)
(1) 1.0 m
(2) 4.2 m
(3) 6.1 m
(4) 9.8 m

A plane is inclined at an angle $\alpha = 30 ^ { \circ }$ with respect to the horizontal. A particle is projected with a speed $\mathrm { u } = 2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, from the base of the plane, making an angle $\theta = 15 ^ { \circ }$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to: (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
(1) 20 cm
(2) 18 cm
(3) 14 cm
(4) 26 cm