Home
Class 11
PHYSICS
An enemy plane is flying horizontally at...

An enemy plane is flying horizontally at an altitude of `2km` with a speed of `300 ms^(-1)`.An army man with an anti-aircraft gun on the ground sights enemy plane when it is directly overhead and fires a shell with a muzzle speed of `600ms^(-1)`.At what angle with the vertical should the gun be fired so as to hit the plane?

Text Solution

Verified by Experts

Let G be the position of the gun and E that of the enemy plane flying horizontal with speed.

`u=300ms^(-1)`, when the shell is fired with a speed
`v_(0), v_(x)=v_(0) cos theta`
The shell will hit the plane, if the horizontal distance EP travelled by the plane in time t= the distance travelled by the shell in the horizontal direction in the same time, i.e.
`uxxt=v_(x)xxt" or u=v_(x) rArr u=v_(0) cos theta`
or `cos theta=(u)/(v_(0))=(300)/(600)=0.5" or "theta=60^(@)`
Therefore, angle with the vertical `=90^(@)-theta=30^(@)`
Promotional Banner

Similar Questions

Explore conceptually related problems

An enemy air plane is flying horizontally at an altitude of 2.7km with a speed of 250ms^(-1) .An army man on the ground observed it when it is directly over his head.He fired an anti-aircraft gun with a muzzle speed of 500ms^(-1) ,such that the shell hits the plane.At what angle with the horizontal,gun should be fired?

A fighter plane flying horizontally at an altitude of 2km with speed of 540 kmph passes directly over head an anti aircraft gun.If the gun can fire a bullet at the muzzle speed of 500ms^( - 1) ,at what angle with the vertical the gun should fire the bullet so that the bullet hits the plane?

A fightre plane flying horizontally at an altitude oa 1.5 km with speed 720 h^(-1) passes directly over head an anticraft gun. At what angle from the vertical should the gun be fired from the shell with muzzle speed 600 ms^(-1) to hit plane. At what minimum altitude showld the pilot fly the plane to avoid being hit ? ( Take g= 10 ms^(-2)).

A fighter plane flying horizontally at an altitude of 1.5 km with speed of 720 km h^9-10 passes directlu overhead an anticraft gun. At what anle fro the gun with muzzle speed 400 ms^(-1) to hit the plane in shortest time ?

A helicopter is flying horizontally at an altitude of 2km with a speed of 100 ms^(-1) . A packet is dropped from it. The horizontal distance between the point where the packet is dropped and the point where it hits the ground is (g = 10 ms^(-2))

A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 kmh^(-1) . At what angle of sight (w.r.t horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target? (Take g=10ms^(-2))

A jet plane files horizonally at a height h at a speed v. An anti-aircraft gun fires a shell at the plane when it is vertically above the gun. Show that the minimum muzzle speed required to hit the plane is sqrt(v^(2)+2gh) at an angle tan^(-1)sqrt(2gh)/(v)

A bullet of mass 50 kg is fired by a gun of mass 5 kg .If the muzzle speed of the bullet is 200 ms^(-1) , what is the recoil speed of the gun?

A plane flying horizontally at 100 m s^-1 releases an object which reaches the ground in 10 s . At what angle with horizontal it hits the ground ?