(C) Given: Height $h = 80 \ m$, initial horizontal velocity $v = 8 \ ms^{-1}$, and acceleration due to gravity $g = 10 \ ms^{-2}$.For vertical motion,

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(C) Given: Height $h = 80 \ m$, initial horizontal velocity $v = 8 \ ms^{-1}$, and acceleration due to gravity $g = 10 \ ms^{-2}$.For vertical motion, the time taken to reach the ground is given by the equation $h = \frac{1}{2}gt^2$.Substituting the values: $80 = \frac{1}{2} \times 10 \times t^2$.$80 = 5t^2 \implies t^2 = 16 \implies t = 4 \ s$.For horizontal motion, the distance $d$ covered is given by $d = v \times t$.Substituting the values: $d = 8 \times 4 = 32 \ m$.Thus, the time $t$ is $4 \ s$ and the distance $d$ is $32 \ m$.

Class 11 Physics 2 Motion in a Plane Horizontal Projectile Motion

Medium

From the top of a tower, $80 \ m$ high from the ground, a stone is thrown in the horizontal direction with a velocity of $8 \ ms^{-1}$. The stone reaches the ground after a time $t$ and falls at a distance of $d$ from the foot of the tower. Assuming $g=10 \ ms^{-2}$, the time $t$ and distance $d$ are given respectively by

WBJEE 2012 All WBJEE

A
$6 \ s, 64 \ m$
B
$6 \ s, 48 \ m$
C
$4 \ s, 32 \ m$
D
$4 \ s, 16 \ m$

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2 Motion in a Plane

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Horizontal Projectile Motion

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$A$ ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight,its kinetic energy will be

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On a planet, a particle is thrown with a velocity $\vec{V} = 6 \hat{i} + (20 - 4t) \hat{j}$. Match the lists. (All quantities are in $SI$ units)
$P$. Time of flight $1$. $3$
$Q$. Time when particle is moving at an angle of $53^{\circ}$ with horizontal in upwards direction $2$. $10$
$R$. Range of the particle $3$. $50$
$S$. Maximum height reached by the particle $4$. $60$

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$P$. Time of flight	$1$. $3$
$Q$. Time when particle is moving at an angle of $53^{\circ}$ with horizontal in upwards direction	$2$. $10$
$R$. Range of the particle	$3$. $50$
$S$. Maximum height reached by the particle	$4$. $60$

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$A$ particle is projected from point $O$ with velocity $u$ at an angle $\alpha$ with the horizontal. If at point $P$,its velocity is perpendicular to the initial direction of projection,then find the time taken to reach from $O$ to $P$.

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