JEE

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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Class 11, Friction, JEE, Laws of Motion

An inclined plane is bent in such a way that the vertical cross-section is given by 𝑦 = 𝑥²/4, where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ = 0.5, determine the greatest vertical height (in cm) at which the block can remain at rest without sliding down the surface.

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