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Projectile motion
Class 11, Motion in a plane, NEET, Projectile Motion

A projectile is thrown at angles θ and (90 − θ) with the horizontal with the same speed of 20 ms⁻¹ from the same point of projection. If difference between the individual heights attained by them is 5 m, then the individual heights are, respectively, (g = 10 ms⁻²)

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pendulum
2022, Class 11, Conservation of energy, Mains, Work, Energy, and Power

The pendulum is suspended by a string a length 250 cm. The bob has a mass of 200 g and is displaced sideways such that the string makes an angle of 60° with the vertical, as illustrated. Upon releasing the bob from this position, determine the maximum speed (in m/s) it achieves during its motion.

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student skates
2020, Advanced, Class 11, Conservation of energy, JEE, Work, Energy, and Power

A student skates up a ramp that makes an angle of 30° with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v₀ and wants to turn around over a semicircular path xyz of radius R, during which he/she reaches a maximum height h (at point y) from the ground, as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

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motorboat
Class 11, JEE, Motion in a straight line, NEET, Relative velocity in 1D

A motor boat moving downstream overcame a raft at a point A; after τ (Tau) min, it turned back and after some time, met the raft again at a distance l = 6 km from point A. Calculate flow of velocity assuming the speed of the boat is constant.

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