Two spherical balls having equal masses with | vedclass

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

Question

(D) Let the first ball be thrown at $t = 0$ and the second ball at $t = 3 \, 	ext{s}$.Let $t$ be the time elapsed since the first ball was thrown.The

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(D) Let the first ball be thrown at $t = 0$ and the second ball at $t = 3 \, 	ext{s}$.Let $t$ be the time elapsed since the first ball was thrown.The position of the first ball is $y_1 = u t - \frac{1}{2} g t^2 = 35 t - 5 t^2$.The position of the second ball is $y_2 = u(t - 3) - \frac{1}{2} g(t - 3)^2 = 35(t - 3) - 5(t - 3)^2$.At the point of collision, $y_1 = y_2$.$35 t - 5 t^2 = 35(t - 3) - 5(t^2 - 6 t + 9)$$35 t - 5 t^2 = 35 t - 105 - 5 t^2 + 30 t - 45$$0 = 30 t - 150$$30 t = 150 \implies t = 5 \, 	ext{s}$.Substituting $t = 5 \, 	ext{s}$ into the equation for $y_1$:$h = 35(5) - 5(5)^2 = 175 - 125 = 50 \, 	ext{m}$.Thus, the balls collide at a height of $50 \, 	ext{m}$.

Similar Questions

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights $a$ and $b$. The ratio of the time taken by the two to cover these distances is

$A$ stone is dropped from a building of height $h$ and it reaches the ground after $t$ seconds. From the same building,if two stones are thrown (one upwards and one downwards) with the same velocity $u$ and they reach the earth's surface after $t_1$ and $t_2$ seconds respectively,then:

$A$ player throws a ball upwards with an initial speed of $29.4 \; m s^{-1}$. To what height does the ball rise and after how long (in seconds) does the ball return to the player's hands? (Take $g = 9.8 \; m s^{-2}$ and neglect air resistance).

The distance covered by a stone dropped from the top of a building in the last second of its motion is $0.36$ times the total distance travelled by it. The height of the building is (acceleration due to gravity $g = 9.8 \ m/s^2$). (in $m$)

Find the speed of a body at the ground when it falls freely from a height of $2\,m$. $(g = 10\,ms^{-2})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module