HARD
JEE Main/Advance
IMPORTANT
Earn 100

The benches of a gallery in a cricket stadium are 1 m wide and 1 m high. A batsman strikes the ball at a level of 1 m above the ground and hits a mammoth sixer. The ball starts at 35 m s-1 at an angle of 53° with the horizontal. The benches are perpendicular to the plane of motion and the first bench is 110 m from the batsman. On which bench will the ball hit?

Important Questions on Kinematics

HARD
JEE Main/Advance
IMPORTANT
A ship is approaching a cliff of height 105 m above sea level. A gun fitted on the ship can fire shots with a speed of 110 m s-1. Find the maximum distance from the foot of the cliff from where the gun can hit an object on the top of the cliff. g=10m s-2
MEDIUM
JEE Main/Advance
IMPORTANT
Shots fired simultaneously from the top and bottom of a vertical cliff with the elevation α and β respectively, strike an object simultaneously at the same point on the ground. If s is the horizontal distance of the object from the cliff, then what is the height of the cliff. (β>α)
MEDIUM
JEE Main/Advance
IMPORTANT
Some students are playing cricket on the roof of a building of height 20 m. While playing, a ball falls on the ground. A person on the ground returns their ball with the minimum possible speed at angle of projection 45° with the horizontal. The speed of projection is 20α m s-1. Here α is an integer. Find α.
MEDIUM
JEE Main/Advance
IMPORTANT
A cannon fires successively two shells with velocity v0=250 m s-1; the first at the angle θ1=53° and the second at the angle θ2=37° to the horizontal, in the same vertical plane, neglecting the air drag, find the time interval (in sec) between firings leading to the collision of the shells. g=10 m s-2
HARD
JEE Main/Advance
IMPORTANT

A small cannon A is mounted on a platform (which can be rotated so that the cannon can aim at any point) and is adjusted for the maximum range R of shells. It can throw shells at any point on the shown circle (dotted) on the ground. Suddenly a wind storm starts blowing in a horizontal direction normal to AB with a speed 2 times the velocity of the shell. At what least distance can the shell land from point B. (Assume that the velocity of the wind storm is imparted to the shell in addition to its velocity of projection. Also, assume that the platform is kept stationary while projecting the shell.)

Question Image

HARD
JEE Main/Advance
IMPORTANT

A body A falls freely from some altitude H(<<Re). At the moment the first body starts falling another body B is thrown from the earth's surface, which collides with the first at an altitude h=H2. The horizontal distance of that point of collision is l from the starting point of B. Find the initial velocity and the angle at which it was thrown?

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HARD
JEE Main/Advance
IMPORTANT
Two guns situated on the top of a hill of height 10 m fire one shot each with the same speed 53 m s-1 at some interval of time. One gun fires horizontally and other fires upwards at an angle of 60° with the horizontal. The shots collide in the air at point P. Find :-
(a). The time interval between the firings and
(b). The coordinates of the point P. Take the origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in x-y plane.
MEDIUM
JEE Main/Advance
IMPORTANT
A small ball rolls of the top of a stairway 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 will strike the nth step where n is equal to (assume ball strike at the edge of the step).