Q94
Projectiles
Clearing an Obstacle or Passing Through a Point
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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) $50 \mathrm{~m/s}$.