Question

Ball is A is dropped from the top of a building At the same instant ball B is thrown vertically upwards from the ground. When the balls collide, they are moving in opposite directions and the speed of A is twice the speed of B. At what fraction of the height of the building did the collision occurs??
a) 1/3
b) 2/3
c) 1/4
d) 2/5
​

Answer 1

Answer:

abcd find answerhih7ohyivyiv8y

Answer 2

Cᴏʀʀᴇᴄᴛ Qᴜᴇsᴛɪᴏɴ :-

• Ball is A is dropped from the top of a building At the same instant ball B is thrown vertically upwards from the ground. When the balls collide, they are moving in opposite directions and the speed of A is twice the speed of B. At what fraction of the height of the building did the collision occurs?

Aɴsᴡᴇʀ :-

$\sf\large\pink{★\:Height = 2/3}$

Sᴏʟᴜᴛɪᴏɴ :-

• The distance travelled by the two balls,

$\sf\large\purple{→ h = ut - \frac{1}{2} {gt}^{2} }$

$\sf\large\purple{→ H - h = \frac{1}{2} {gt}^{2} }$

• Take their ratio,

$\sf\large\purple{→ \frac{h}{H - h} = \frac{2u}{gt} - 1 }$ ⠀⠀⠀⠀(1)

• Let $\sf{u}_{a}$ and $\sf{u}_{g}$ be the velocities at collision,then $\sf{g}{t}$ is related to them via,

$\sf\large\purple{→ gt = u - {u}_{b} = {u}_{a} }$ ⠀⠀(2)

• And at collision,

$\sf\large\purple{ → {u}_{g} = {2}_{ub} }$ ⠀⠀⠀⠀⠀⠀⠀(3)

• From 2 and 3 , we get $\sf\large{ u = {3}_{ub} }$ which leads to,

$\sf\large\purple{→ gt = u - {u}_{b} = \frac{2}{3} u }$

• Plug above gt into (1) to get,

$\sf\large\purple{ → \frac{h}{H - h} = \frac{2}{1} }$

• Thus,they colide at,

${\boxed{{\bf{∴Height = \frac{2}{3} h }}}}$