A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be
Parabolic
Inclined straight line
Vertical straight line
Horizontal straight line
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
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 |
$(D)$ Vertical displacement | $(s)$ $20$ SI unit |
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?
($AV$) $\vec{u}_0=\sqrt{2 g h} \hat{x}$ ($B$) $\vec{v}=\sqrt{2 g h}(\hat{x}-\hat{z})$ ($C$) $\theta=60^{\circ}$ ($D$) $d / h_1=2 \sqrt{3}$
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?