A large number of bullets are fired in all di | vedclass

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

Question

(B) The horizontal range $R$ of a projectile fired with speed $u$ at an angle $	heta$ is given by $R = \frac{u^2 \sin(2	heta)}{g}$.The maximum horiz

Vedclass · Accepted Answer

$\frac{\pi u^4}{g^2}$

Vedclass · Answer

(B) The horizontal range $R$ of a projectile fired with speed $u$ at an angle $	heta$ is given by $R = \frac{u^2 \sin(2	heta)}{g}$.The maximum horizontal range $R_{max}$ occurs when $	heta = 45^\circ$,which is $R_{max} = \frac{u^2}{g}$.Since the bullets are fired in all directions,they will cover a circular area on the ground with the radius equal to the maximum range $R_{max}$.The area $A$ of this circle is $A = \pi R_{max}^2$.Substituting the value of $R_{max}$,we get $A = \pi \left(\frac{u^2}{g}ight)^2 = \frac{\pi u^4}{g^2}$.

$A$ large number of bullets are fired in all directions with the same speed $u$. The maximum area of the ground on which these bullets spread is ($g$ - acceleration due to gravity).

Similar Questions

In the motion of a projectile moving freely under gravity,which of the following is true?

The angle of projection of a projectile for which its initial kinetic energy becomes half at its maximum height is (in $^{\circ}$)

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = 8t - 5t^2 \text{ m}$ and $x = 6t \text{ m}$,where $t$ is in seconds. The velocity with which the projectile is projected is (in $\text{ m/s}$)

$A$ gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is $6.4 \text{ m}$. The speed of the bullets from the gun is . . . . . . m/s. (take $g = 10 \text{ m/s}^2$)

$A$ bullet is fired from a cannon with a velocity of $500 \, m/s$. If the angle of projection is $15^\circ$ and $g = 10 \, m/s^2$,then the horizontal range is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module