EASY
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At what point of the trajectory of projectile the speed is minimum.

Important Questions on Motion in a Plane

MEDIUM
Two projectiles P and Q thrown with velocities v and v2 respectively have the same range. If Q is thrown at an angle of 15° to the horizontal, P must be thrown at an angle of
EASY
A boy is standing on top of a tower of height, 85 m and throws a ball in the vertically upward direction with a certain speed. If 5.25 s later he hears the ball hitting the ground, then the speed with which the boy threw the ball is (take g=10 m s-2, the speed of sound in air is 340 m s-1)
MEDIUM
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is:
MEDIUM
A projectile is given an initial velocity of i^+3 j^ m s-1, where i^ is along the ground and j^ is along the vertical. Then, the equation of the path of projectile is [Take, g=10 m s-2
EASY

The velocity of a projectile at the initial point A is 2i^-3j^ m s-1. Its velocity (in m s-1) at point B is

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MEDIUM
A stone is projected with velocity 2gh, so that it just clears two walls of equal height h, at distance of 2h from each other. The time interval of passing between the two walls is
HARD
A ball is thrown from ground at an angle θ with horizontal and with an initial speed u0. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is V1. After hitting the ground, ball rebounds at the same angle θ but with a reduced speed of u0α. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is 0.8V1, the value of α is______

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HARD
Two objects are located at height 10 m above the ground. At some point of time, the objects are thrown with initial velocity 22 m s-1 at an angle 45° and 135° with the positive X-axis respectively. Assuming g=10 m s-2, the velocity vectors will be perpendicular to each other at time equal to
HARD

Two particles are simultaneously projected in the horizontal direction from a point P at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point P) are mutually perpendicular, is:

HARD
A mobile phone of mass 100 g falls from the hand of a person through the window of a train. The train is accelerating at 1 m s-2 and just 20 s have passed since it left the station from standstill. If the window is 2 m above the ground. With what kinetic energy will the phone will hit the ground? g=10 m s-2
EASY
Four projectiles are fired with the same velocities at angles 25°,40°,55° and 70° with the horizontal. The range of projectile will be largest for the one projected at angle _____.
EASY
Two bodies are projected at angles θ and 90o-θ to the horizontal with the same speed. The ratio of their times of flight is
HARD
A particle aimed at a target, projected at an angle 15° with the horizontal is short of the target by 10 m. If the same particle projected at an angle of 45° with the horizontal then it is away from the target by 15 meters. The angle of projection to hit the target is
HARD
The horizontal range and maximum height attained by a projectile are R and H respectively. If a constant horizontal acceleration a=g4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be 
EASY
A man of height 7.33 ft releases a stone from the slingshot just above his head. If the stone travels in a vertical direction towards the sky with velocity of 10 m s-1, then the time it takes to reach the ground is (Assume acceleration due to gravity g=10 m s-2)
HARD
A wheel of radius R is trapped in a mud pit and spinning. As the wheel is spinning, it splashes mud blobs with initial speed u from various points on its circumference. The maximum height from the centre of the wheel, to which a mud blob can reach is
HARD
Points P,Q and R are in a vertical line such that PQ=QR. A ball at P is  allowed to fall freely with zero initial speed. The ratio of the times of descent through PQ and QR is
EASY
Which of the following graphs represents the speed v of a vertical projectile as a function of time t?
MEDIUM
Two balls are projected at an angle θ and (90°-θ) with respect to the horizontal with the same speed. The ratio of their maximum vertical heights is
HARD
A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce (in meters) is _____________.