Part 4-Motion in a plane hard

A circular disc of radius r = 5m is rotating in horizontal plane about y-axis. Y-axis is vertical axis passing through the centre of disc and x-z is the horizontal plane at ground. The height of disc above ground is h = 5 m. Small particles are ejecting from disc in horizontal direction with speed 12 m/s from the circumference of disc then the distance of these particles from origin when they hits the x-z plane is -

Two bullets are thrown simultaneously in the same vertical plane from same point with different speeds u₁ and u₂ at angles of projection θ₁ and θ₂  with horizontal such that u₁cosθ₁ = u₂ cosθ₂ then the path followed by one as seen from other is a -

A ball is projected upwards from the top of the tower with a velocity 50 ms^–1 making an angle 30° with the horizontal. The height of tower is 70 m. After how many seconds the ball will strike the ground?

A projectile is fired at an angle of 30º to the horizontal such that the vertical component of its initial velocity is 80 m/s. Its time of flight is T. Its velocity at t = T/4 has a magnitude of nearly :

Consider a boy on a trolley who throws a ball with speed 20 m/s at an angle 37º with respect to trolley in direction of motion of trolley which moves horizontally with speed 10 m/s then what will be maximum distance travelled by ball parallel to road -

Path of a projectile fixed at angle 60º with horizontal with velocity 10 m/s as seen from other projectile fixed at angle 30º with horizontal will be (during the time both projectile are in air)-

A passenger, observer A, in a car traveling at a constant horizontal velocity of magnitude 60 mi/h pour a cup of coffee for the tired driver. Observer B stands on the side of the road and watches the pouring process through the window of the car as it passes. Which observer(s) sees a parabolic path for the coffee as it moves through the air ?

Identify the correct statement related to the projectile motion -

If T₁ and T₂ are the times of flight for two complementary angles, then the range of projectile R is given by -

A ball is projected with a velocity 20 ms^–1 at an angle to the horizontal. In order to have the maximum range, its velocity at the highest position must be -

A stone is projected with speed u and an angle q with the horizontal from a high tower, then-

(i) Range of stone = u² sin2θ/g

(ii) Time of flight = 2u sin θ/g

Select correct one

A stone thrown with the velocity V₀ = 14 m/s at an angle 45° to the horizontal, dropped to the ground at a distance 'S' from the point where it was thrown. From what height should the stone be thrown in horizontal direction with the same initial velocity so that it fall at the same spot -

A particle is projected up the inclined such that its component of velocity along the incline is 20 m/s. Time of flight is 4 sec. Horizontal displacement of the particle in 4 sec is 64 m. The angle made by the incline with the horizontal is –

Two projectile thrown from the same point at angles 60⁰ and 30⁰ with the horizontal attain the same The ratio of their initial velocities is -

A ball rolls off the top of a strairway horizontally with a velocity of 4.5 m s^–1. Each step is 0.2 m high and 0.3 m wide. If g is 10 m s^–2, then the ball strike the nth step where n is equal to -

A body is thrown horizontally with a velocity √2gh from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is -

A particle having a mass of 0.5 kg is projected under gravity with a speed of 98 ms^–1 at an angle of 60°. The magnitude of the change of momentum of the particle after 10 s is -

The range of a projectile when launched at an angle 15º with the horizontal is 1.5 km. What will be the range of that projectile when launched with the same velocity at an angle 45º to the horizontal?

A body of mass 1kg crosses a point O with a velocity 60 ms^–1. A force of 10N directed towards O begins to act on it. It will again cross O in -

A large box is moving on horizontal floor with constant acceleration a = g. A particle is projected inside box with velocity u and angle 'θ' with horizontal from box. frame. For the given 'u', the value of 'θ' for which horizontal range inside box will be maximum is -

A ball whose kinetic energy is E, is projected at an angle of 45⁰ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be -