Home
Class 11
PHYSICS
A bullet fired at an angle of 30^@ with ...

A bullet fired at an angle of `30^@` with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away ? Assume the muzzle speed to be fixed, and neglect air resistance.

Text Solution

Verified by Experts

`R = 2 km`
`R _(max) =` ? Horizontal range, ` R = ( u ^(2) sin 2 theta)/( g ) implies 3 = ( u ^(2) sin 60^(@))/( g )`
or `3 = ( u ^(2))/( g ) xx ( sqrt3 )/( 2) implies ( u ^(2))/( g ) = ( 3 xx 2)/( sqrt3).`
Since the muzzle velocity is fixed so the maximum horizontal range,
`R _(max) = ( u ^(2))/( g ) = ( 3 xx 2 )/( sqrt3) xx ( sqrt3)/( sqrt3) = 2 sqrt3 = 3. 464 m.`
Promotional Banner

Similar Questions

Explore conceptually related problems

A bullet of mass m fired at 30^@ to the horizontal leaves the barrel of the gun with a velocity v. The bullet hits a soft target at a height h above the ground while it is moving downward and emerges out with half the kinetic energy it had before hitting the targtet. which of the following statements are correct in respect of bullet after it emerges out of the target?

A police van moving on a highway with a speed of 30 km h^-1 fires a bullet at a thiefs car speeding away in the same direction with a speed of 192 km h^-1 . If the muzzle speed of the bullet is 150 m s^-1 with what speed does the bullet hit the thiefs car ? (Note: Obtain that speed which is relevant for damaging the thief s car).

A cricket bowler releases tha ball in two different ways giving it horizontal velocity and a small downward velocity and the speed v_s at the time of release is the same. Both are relased at a height H from the ground. Which one will have greater speed when the ball hits the ground? Neglect air resistance.

A cricket bowler releases the ball in two different ways (a) giving it only horizontal velocity and (b) giving it horizontal velocity and a small downward velocity. The speed v_s at the time of release is the same . Both are released at a height H from the ground . which one will have greater speed when the ball hits the ground ? Neglect air resistance.

Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 m s^-1 and 30 m s^-1 . Verify that the graph shown in Fig. 3.27 correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take g = 10 m s^-2 . Give the equations for the linear and curved parts of the plot.

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km//h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s^-1 to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? (Take g = 10 ms^2 ).

A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s^-1 , at right angles to the horizontal component of the earth’s magnetic field, 0.30 xx 10^-4 Wb m^-2 , What is the instantaneous value of the emf induced in the wire?