question_answer

A plane flying horizontally at a height of 1500 meters with a speed of 200 meter/second passes directly over an aircraft gun. Then the angle with the horizontal at which the shell should be fired from the gun with a muzzle velocity of 400 meters per second to hit the plane is:

A) \[90{}^\circ \]

B) \[60{}^\circ \]

C)   \[30{}^\circ \]

D)   \[45{}^\circ \]

Correct Answer: B

Solution :

                      Let the shell hit the plane at the point B after time t (figure) \[200\,t={{v}_{0}}\cos \theta \times t\] \[\cos \theta =\frac{200}{{{v}_{0}}}=\frac{200}{400}=\frac{1}{2}\] \[\therefore \]    \[\theta ={{60}^{o}}\] Hence, the correction option is (d).