A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be

  • A

    Parabolic

  • B

    Inclined straight line

  • C

    Vertical straight line

  • D

    Horizontal straight line

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A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement time graph is characterised by

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An aeroplane is moving with a velocity $u$. It drops a packet from a height $h$. The time $t$ taken by the packet in reaching the ground will be

A particle is projected horizontally from a tower with velocity $10\,m / s$. Taking $g=10\,m / s ^2$. Match the following two columns at time $t=1\,s$.

Column $I$ Column $II$
$(A)$ Horizontal component of velocity $(p)$ $5$ SI unit
$(B)$ Vertical component of velocity $(q)$ $10$ SI unit
$(C)$ Horizontal displacement $(r)$ $15$ SI unit
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A slide with a frictionless curved surface, which becomes horizontal at its lower end,, is fixed on the terrace of a building of height $3 h$ from the ground, as shown in the figure. A spherical ball of mass $\mathrm{m}$ is released on the slide from rest at a height $h$ from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_0=u_0 \hat{x}$ and falls on the ground at a distance $d$ from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\overrightarrow{\mathrm{v}}$ and reaches a maximum height $h_l$. The acceleration due to gravity is $g$ and the coefficient of restitution of the ground is $1 / \sqrt{3}$. Which of the following statement($s$) is(are) correct?

($AV$) $\vec{u}_0=\sqrt{2 g h} \hat{x}$ ($B$) $\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$  ($C$) $\theta=60^{\circ}$  ($D$) $d / h_1=2 \sqrt{3}$

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A helicopter is flying horizontally with a speed $'v'$ at an altitude $'{h}'$ has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

  • [JEE MAIN 2021]