Motion in a Plane

A fighter plane flying horizontally at an altitude of 1.5 km with speed of 720 km/h passes directly overhead an anticraft gun. At what angle from the vertical should the gun be fixed for the shell with muzzle speed 400 m/s to hit the plane? 

The speed of a projectile when it is at its greatest height is √(2/5) times its speed at half the maximum height. What is its angle of projection?

In long jump, does it matter how high you jump? What factors determine the span of the jump? 

A ball of mass m is thrown vertically up. Another ball of mass 2 m is thrown at an angle with the vertical. Both of them stay in air for the same period of time. What is the ratio of the height attained by the two balls. 

A skilled gunman always keeps his gun slightly tilted above the line of sight while shooting. Why?

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. What will the percentage increase in the horizontal range?

Two bodies were thrown simultaneously from the same point, one straight up and the other at an angle θ = 60° to the horizontal. The initial velocity of each body is u = 30 m/s. Neglecting air resistance, find the distance between the bodies after 2 seconds.

From the top of a tower 156.8 m high a projectile is thrown up with a velocity of 39.2 ms^–1, making an angle 30° with horizontal direction. Find the distance from the foot of tower where it strikes the ground and the time taken by it to do so.

A hunter aims his gun and fires a bullet directly at a monkey in a tree. At the instant the bullet leaves the barrel of the gun, the monkey drops. Will the bullet hit the monkey. Substantiate your answer with proper reasoning. 

A boy stands at 78.4 m from a building and throws a ball which just enters a window 39.2 m above the ground. Calculate the velocity of projection of the ball.