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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:

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Important Questions on Kinematics

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Two guns A and B can fire bullets at speeds 1 km s-1 and 2 km s-1 respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:
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The position of a projectile launched from the origin at t = 0 is given by r = 4 i ^ + 5 j ^ m   at t = 2s. If the projectile was launched at an angle θ  from the horizontal, then θ   is (take g = 10 ms-2).
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A body is projected at an angle of 60° with the horizontal such that the vertical component of its initial velocity is 40 m s-1. The magnitude of velocity of the projectile at one quarter of its time of flight is nearly (Acceleration due to gravity =10 m s-2)
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Two long parallel plates A and B are separated by a distance of 4 cm with an electric field of 45.5 V m-1 between the plates directed normally from plate A to plate B, as shown in the figure. An electron is projected from plate A with velocity v at an angle of 30° with the surface of plate A. The maximum value of v so that the electron does not hit plate B is
(Assume gravity free space, charge of electron =1.6×10-19C and mass of electron =9.1×10-31 kg

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Two towers A and B, each of height 20 m are situated a distance 200 m apart. A body thrown horizontally from the top of the tower A with a velocity 20 ms-1 towards the tower B hits the ground at point P and another body thrown horizontally from the top of tower B with a velocity 30 ms-1 towards the tower A hits the ground at point Q. If a car starting from rest from P reaches Q in 10 seconds, the acceleration of the car is _________ (Acceleration due to gravity =10 ms-2)
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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
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An aeroplane is flying in a horizontal direction with a velocity u and at a height of 2000 m. When it is vertically below a point A on the ground a food packet is released from it. The packet strikes the ground at point B. If AB=3 km and g=10 m s-2, then the value of u is
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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)