Question

Two bodies A and B are projected from the same place in same vertical
plane with velocities v1 = 10m/s and v2 = 5m/s from a long
inclined plane as shown. Find the ratio of their times of flight._
1²
vi is in horizontal direction​

Answer 1

Given :-

◉ Two bodies A and B are projected from the same point with velocities v₁ = 10 m/s & v₂ = 5 m/s from a long inclined plane as shown.

Note: Please refer to the attachment for the diagram.

To Find :-

◉ Ratio of thier times of flight.

Solution :-

Let the angle between the horizontal and inclined plane be β and the angle between trajectory and horizontal be ɑ

We have,

⇒ Time of flight = 2 u sin(ɑ - β) / gcosβ

For object A,

⇒ T₁ = 2 × v₁ × sin(ɑ - β) / gcosβ

⇒ T₁ = 2×10×sin(ɑ - β) / gcosβ

⇒ T₁ = 20sin(ɑ - β) / gcosβ ...(1)

Similarly, For Object B,

⇒ T₂ = 2 × v₂ × sin(ɑ - β) / gcosβ

⇒ T₂ = 2×5×sin(ɑ - β) / gcosβ

⇒ T₂ = 10sin(ɑ - β) / gcosβ ...(2)

Now, We have to find the ratio of time of flight of Object A to Object B.

⇒ T₁ / T₂ = { 20sin(ɑ - β) / gcosβ } / { 10sin(ɑ - β) / gcosβ }

⇒ T₁ / T₂ = 20sin(ɑ - β) / 10sin(ɑ - β)

⇒ T₁ / T₂ = 20 / 10

⇒ T₁ / T₂ = 2 / 1

Hence, The ratio of time of flight of Object A to Object B is 2 : 1

Answer 2

$<font color= pink>$

SOLUTION:-

$<font color= red>$

☞ uBy = 50 sin a

☞ A and B reach the same height at same time

$<font color= orange>$

☞ condition for collision

☞ uAy = uBy

30°

$<font color= green>$

☞ 50sin³

☞ a = sin