A body is projected from the ground at an ang | vedclass

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

Question

(B) Let the initial velocity be $v_1$. The initial kinetic energy is $K = \frac{1}{2} m v_1^2$.In projectile motion,the horizontal component of veloci

Vedclass · Accepted Answer

$K\left( 1 - \frac{\cos^2 	heta_1}{\cos^2 	heta_2} ight)$

Vedclass · Answer

(B) Let the initial velocity be $v_1$. The initial kinetic energy is $K = \frac{1}{2} m v_1^2$.In projectile motion,the horizontal component of velocity remains constant throughout the flight.Therefore,$v_1 \cos 	heta_1 = v_2 \cos 	heta_2$,where $v_2$ is the velocity at angle $	heta_2$.From this,$v_2 = \frac{v_1 \cos 	heta_1}{\cos 	heta_2}$.The kinetic energy at angle $	heta_2$ is $K' = \frac{1}{2} m v_2^2 = \frac{1}{2} m \left( \frac{v_1 \cos 	heta_1}{\cos 	heta_2} ight)^2$.$K' = \left( \frac{1}{2} m v_1^2 ight) \frac{\cos^2 	heta_1}{\cos^2 	heta_2} = K \frac{\cos^2 	heta_1}{\cos^2 	heta_2}$.By the law of conservation of mechanical energy,the gain in potential energy $(PE)$ is equal to the loss in kinetic energy.$PE = K - K' = K - K \frac{\cos^2 	heta_1}{\cos^2 	heta_2} = K \left( 1 - \frac{\cos^2 	heta_1}{\cos^2 	heta_2} ight)$.

$A$ body is projected from the ground at an angle $\theta_1$ with the horizontal with kinetic energy $K$. What is the potential energy of the body when the velocity makes an angle $\theta_2$ with the horizontal?

Similar Questions

$A$ small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track,the normal reaction is maximum in

$A$ particle moving in $x-y$ plane starts from the origin at $t=0$ with an initial velocity $(-\hat{i}+\hat{j}) \,ms^{-1}$ and undergoes an acceleration of $(6 \hat{i}+4 \hat{j}) \,ms^{-2}$. Its displacement after $2 \,s$ is (in $\,m$)

$A$ particle is moving in a circle:

$A$ particle has an initial velocity of $(\hat{i} + \hat{j}) \, m/s$ and an acceleration of $(\hat{i} + \hat{j}) \, m/s^2$. Its speed after $10 \, s$ will be:

$A$ cricketer can throw a ball to a maximum horizontal distance of $100\,m$. With the same speed,how high above the ground can the cricketer throw the same ball (in $,m$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module