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The maximum speed of a boat in still water is \( 27 \, \text{km/h} \). Now this boat is moving downstream in a river flowing at \( 9 \, \text{km/h} \). A man in the boat throws a ball vertically upwards with speed of \( 10 \, \text{m/s} \). Range of the ball as observed by an observer at rest on the river bank, is ______ cm. (Take \( g = 10 \, \text{m/s}^2 \) )

A sportsman runs around a circular track of radius \( r \) such that he traverses the path \( ABAB \). The distance travelled and displacement, respectively, are:

A particle is projected at an angle of \( 30^\circ \) from horizontal at a speed of \( 60 \, \text{m} / \text{s} \). The height traversed by the particle in the first second is \( h_0 \) and height traversed in the last second, before it reaches the maximum height, is \( h_1 \). The ratio \( h_0 : h_1 \) is ______. \([ \, \text{Take}, \, g = 10 \, \text{m} / \text{s}^2 ]\)

A ball of mass \( 100 \, \text{g} \) is projected with velocity \( 20 \, \text{m/s} \) at \( 60^\circ \) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

Two projectiles are fired with same initial speed from same point on ground at angles of \( (45^\circ - \alpha) \) and \( (45^\circ + \alpha) \), respectively, with the horizontal direction. The ratio of their maximum heights attained is:

A body of mass $2 \text{ kg}$ moving with velocity of $\vec{v}_{\text{in}} = 3\hat{i} + 4\hat{j} \text{ m s}^{-1}$ enters into a constant force field of $6 \text{ N}$ directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ seconds, then velocity of the body when it emerges from force field is:

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is \( 8 \) times higher than that of the second ball. \( T_1 \) and \( T_2 \) are the total flying times of first and second ball, respectively, then the ratio of \( T_1 \) and \( T_2 \) is:

Two projectiles are fired from ground with same initial speeds from same point at angles \( (45^\circ + \alpha) \) and \( (45^\circ - \alpha) \) with horizontal direction. The ratio of their times of flights is:

A particle is projected with velocity \( u \) so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \( \frac{n u^{2}}{25 g} \), where value of \( n \) is: (Given, '\( g \)' is the acceleration due to gravity.)

A helicopter flying horizontally with a speed of \( 360 \, \text{km}/\text{h} \) at an altitude of \( 2 \, \text{km} \), drops an object at an instant. The object hits the ground at a point O, \( 20 \, \text{s} \) after it is dropped. Displacement of ‘O’ from the position of helicopter where the object was released is:
(use acceleration due to gravity \( g = 10 \, \text{m}/\text{s}^2 \) and neglect air resistance)

The angle of projection of a particle is measured from the vertical axis as \( \phi \) and the maximum height reached by the particle is \( h_{m} \). Here \( h_{m} \) as function of \( \phi \) can be presented as:

A ball having kinetic energy \( KE \), is projected at an angle of \( 60^\circ \) from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

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JEE Main 2025 22nd Jan Evening Shift

A ball of mass \( 100 \, \text{g} \) is projected with velocity \( 20 \, \text{m/s} \) at \( 60^\circ \) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is: