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Battles

An aero plane...

Question

An aero plane is flying with speed $60 \frac{m}{s}$ at angle $30^{\circ}$ with the horizontal. A shell is fired horizontally from the aero plane. Find the direction and magnitude of velocity of the shell so that it falls vertically along a straight line with respect to the observer on the ground.

horizontally opposite to motion of plane with velocity

30 \sqrt{3} \frac{m}{s}

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horizontally opposite to motion of plane with velocity

60 \frac{m}{s}

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at angle

30^{\circ}

with the horizontal opposite to motion of plane with velocity

60 \frac{m}{s}

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at angle

30^{\circ}

with the horizontal opposite to motion of plane with velocity

30 \sqrt{3} \frac{m}{s}

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Solution

The correct option is A horizontally opposite to motion of plane with velocity $30 \sqrt{3} \frac{m}{s}$

Component of velocity of aero plane in vertical and horizontal directions are shown in the figure.
Hence,
For the shell to fall along a straight line with respect to the observer on the ground horizontal component of velocity of shell with respect to ground to must be zero
Therefore,
For this shell must be fired horizontal opposite direction with speed of aero plane in horizontal
$V_{B} = 30 \sqrt{3} \frac{m}{s}$
Direction is horizontally opposite to motion of plane.

Final Answer: $(a)$

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An aero plane is flying with speed 60ms at angle 30∘ with the horizontal. A shell is fired horizontally from the aero plane. Find the direction and magnitude of velocity of the shell so that it falls vertically along a straight line with respect to the observer on the ground.

An aero plane is flying with speed $60 \frac{m}{s}$ at angle $30^{\circ}$ with the horizontal. A shell is fired horizontally from the aero plane. Find the direction and magnitude of velocity of the shell so that it falls vertically along a straight line with respect to the observer on the ground.