(C) The vertical displacement $y$ of a projectile at any time $t$ is given by $y = (u \sin \theta)t - \frac{1}{2}gt^2$.Since the particle is at the sa

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(C) The vertical displacement $y$ of a projectile at any time $t$ is given by $y = (u \sin \theta)t - \frac{1}{2}gt^2$.Since the particle is at the same height at times $t_1$ and $t_2$,we have:$(u \sin \theta)t_1 - \frac{1}{2}gt_1^2 = (u \sin \theta)t_2 - \frac{1}{2}gt_2^2$$(u \sin \theta)(t_2 - t_1) = \frac{1}{2}g(t_2^2 - t_1^2)$$u \sin \theta = \frac{g(t_1 + t_2)}{2}$Given $t_1 = 1 \, s$,$t_2 = 3 \, s$,$\theta = 30^{\circ}$,and $g = 10 \, m/s^2$:$u \sin 30^{\circ} = \frac{10(1 + 3)}{2}$$u \times 0.5 = \frac{10 \times 4}{2}$$0.5u = 20$$u = 40 \, m/s$.

Class 11 Physics 2 Motion in a Plane Horizontal Projectile Motion

Medium

$A$ particle is thrown with a velocity of $u \, m/s$ at an angle of $30^{\circ}$ with the horizontal. It passes through points $A$ and $B$ at the same vertical height at times $t_1 = 1 \, s$ and $t_2 = 3 \, s$ respectively,as shown in the figure. The value of $u$ is ....... $m/s$ (take $g = 10 \, m/s^2$).

A
$20$
B
$10$
C
$40$
D
$5$

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Class 11

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2 Motion in a Plane

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Horizontal Projectile Motion

$A$ swimmer dived off a cliff with a running horizontal leap. What must his minimum speed be just as he leaves the top of the cliff so that he will miss the edge at the bottom,given that the ledge at the bottom is $2 \ m$ wide and $10 \ m$ below the top of the cliff?

Medium

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$A$ projectile with speed $50 \ m \ s^{-1}$ is thrown at an angle of $60^{\circ}$ with the horizontal. The maximum height that can be reached is,(acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $m$)

EasyAP EAMCET 2022

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Three projectiles $A, B$ and $C$ are projected at an angle of $30^{\circ}, 45^{\circ}, 60^{\circ}$ respectively. If $R_{A}, R_{B}$ and $R_{C}$ are the ranges of $A, B$ and $C$ respectively,then (velocity of projection is the same for $A, B$ and $C$):

EasyKCET 2016

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$A$ projectile is thrown at an angle of $\pi/3$ with the horizontal,reaching a maximum height $Y$. If another projectile is thrown with the same initial velocity at an angle of $\pi/6$,what will be the maximum height attained?

Medium

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$A$ boy weighing $50 \ kg$ finished a long jump at a distance of $8 \ m$. Considering that he moved along a parabolic path and his angle of jump is $45^{\circ}$,his initial $K.E.$ is (in $J$)

MediumAP EAMCET 2024

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$A$ swimmer dived off a cliff with a running horizontal leap. What must his minimum speed be just as he leaves the top of the cliff so that he will miss the edge at the bottom,given that the ledge at the bottom is $2 \ m$ wide and $10 \ m$ below the top of the cliff?

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