(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 3-2.Motion in 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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Chapter

3-2.Motion in Plane

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Horizontal Projectile Motion

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$,but different maximum heights,$h_1$ and $h_2$. Which of the following is correct?

DifficultAIIMS 2013

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An object is projected such that it attains maximum range. Another body is projected to reach maximum height. If both objects reach the same maximum height,what is the ratio of their initial velocities?

EasyAP EAMCET 2024

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$A$ body is projected at an angle $\theta$ so that its range is maximum. If $T$ is the time of flight,then the value of maximum range is (acceleration due to gravity $= g$)

MediumTS EAMCET 2014

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$A$ bob of mass $0.1\; kg$ hung from the ceiling of a room by a string $2\; m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a)$ at one of its extreme positions,
$(b)$ at its mean position.

Medium

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$A$ projectile thrown with a speed $v$ at an angle $\theta$ has a range $R$ on the surface of the Earth. For the same $v$ and $\theta$,its range on the surface of the Moon will be:

Easy

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Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$,but different maximum heights,$h_1$ and $h_2$. Which of the following is correct?

An object is projected such that it attains maximum range. Another body is projected to reach maximum height. If both objects reach the same maximum height,what is the ratio of their initial velocities?

$A$ body is projected at an angle $\theta$ so that its range is maximum. If $T$ is the time of flight,then the value of maximum range is (acceleration due to gravity $= g$)

$A$ projectile thrown with a speed $v$ at an angle $\theta$ has a range $R$ on the surface of the Earth. For the same $v$ and $\theta$,its range on the surface of the Moon will be:

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