Two balls are projected with the same velocit | vedclass

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

Question

(B) Since the ranges are equal for the same projection velocity,the angles of projection must be complementary.Let the angles be $	heta_1$ and $	het

Vedclass · Accepted Answer

$3h$

Vedclass · Answer

(B) Since the ranges are equal for the same projection velocity,the angles of projection must be complementary.Let the angles be $	heta_1$ and $	heta_2$. Then $	heta_1 + 	heta_2 = 90^{\circ}$.Given $	heta_1 = 30^{\circ}$,therefore $	heta_2 = 90^{\circ} - 30^{\circ} = 60^{\circ}$.The formula for the maximum height of a projectile is $H = \frac{u^2 \sin^2 	heta}{2g}$.For the first ball,$h = \frac{u^2 \sin^2(30^{\circ})}{2g} = \frac{u^2}{2g} \left(\frac{1}{2}ight)^2 = \frac{u^2}{8g}$.For the second ball,$H_2 = \frac{u^2 \sin^2(60^{\circ})}{2g} = \frac{u^2}{2g} \left(\frac{\sqrt{3}}{2}ight)^2 = \frac{u^2}{2g} \cdot \frac{3}{4} = \frac{3u^2}{8g}$.Comparing the two,$H_2 = 3 \left(\frac{u^2}{8g}ight) = 3h$.

Two balls are projected with the same velocity but with different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $30^{\circ}$ and its maximum height is $h$,then the maximum height of the other will be

Similar Questions

$A$ stone is projected from the ground with velocity $50 \, m/s$ at an angle of $30^o$. It crosses a wall after $3 \, s$. How far beyond the wall will the stone strike the ground? $(g = 10 \, m/s^2)$

$A$ particle is projected with velocity $u$ at an angle $\theta$ with the horizontal. What is the change in its velocity at the maximum height?

$A$ projectile is launched from the ground, such that it hits a target on the ground which is $90 \,m$ away. The minimum velocity of the projectile to hit the target is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)

Four objects $P, Q, R,$ and $S$ are projected with the same velocity at angles of $15^o, 30^o, 45^o,$ and $60^o$ respectively. Which of these will have the minimum range?

$A$ ball $P$ is dropped vertically and another ball $Q$ is thrown horizontally with the same initial vertical velocity (which is $0$) from the same height $h$ at the same time. If air resistance is neglected,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module