The equation of motion of a projectile is y = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The standard equation of a projectile is $y = x 	an 	heta - \frac{gx^2}{2u^2 \cos^2 	heta}$.Comparing this with $y = ax - bx^2$,we get $	an

Vedclass · Accepted Answer

$i-d, ii-a, iii-c, iv-b$

Vedclass · Answer

(C) The standard equation of a projectile is $y = x 	an 	heta - \frac{gx^2}{2u^2 \cos^2 	heta}$.Comparing this with $y = ax - bx^2$,we get $	an 	heta = a$ and $b = \frac{g}{2u^2 \cos^2 	heta}$.$i)$ Initial velocity $u$: Since $	an 	heta = a$,$\sec^2 	heta = 1 + a^2$,so $\cos^2 	heta = \frac{1}{1+a^2}$. Substituting into $b$,$b = \frac{g(1+a^2)}{2u^2} \implies u = \sqrt{\frac{g(1+a^2)}{2b}}$. Thus,$i-d$.$ii)$ Range $R$: $y=0 \implies x(a-bx)=0 \implies R = \frac{a}{b}$. Thus,$ii-a$.$iii)$ Max height $H$: $H = \frac{u^2 \sin^2 	heta}{2g} = \frac{u^2 	an^2 	heta \cos^2 	heta}{2g} = \frac{a^2}{4b}$. Thus,$iii-c$.$iv)$ Time of flight $T$: $T = \frac{2u \sin 	heta}{g} = \frac{2u 	an 	heta \cos 	heta}{g} = a \sqrt{\frac{2}{bg}}$. Thus,$iv-b$.Therefore,the correct match is $i-d, ii-a, iii-c, iv-b$.

Column-$I$	Column-$II$
$i)$ The initial velocity of projection	$a)$ $\sqrt{\frac{g(1+a^2)}{2b}}$
$ii)$ The horizontal range of projectile	$b)$ $\frac{a}{b}$
$iii)$ The maximum height attained by projectile	$c)$ $\frac{a^2}{4b}$
$iv)$ The time of flight of projectile	$d)$ $a\sqrt{\frac{2}{bg}}$

Similar Questions

$A$ stone is projected in air. Its time of flight is $3\,s$ and range is $150\,m$. The maximum height reached by the stone is $......\,m$ $\left(g=10\,m/s^2\right)$.

$A$ stone is thrown at an angle $\theta$ to the horizontal reaches a maximum height $H$. Then the time of flight of the stone will be

$A$ body is projected with a speed $u \ m/s$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $3/4$ of the initial kinetic energy. The value of $\beta$ is: (in $^{\circ}$)

$A$ cricketer can throw a ball to a maximum horizontal distance of $100\, m$. The speed with which he throws the ball is ......... $m/s$ (to the nearest integer).

In a sports event,a disc is thrown such that it reaches its maximum range of $80 \ m$. The distance travelled in the first $3 \ s$ is $(g = 10 \ m/s^2)$. (in $m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module