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A particle A is projected with an initial velocity of 60 {~m}

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A particle $A$ is projected with an initial velocity of $60 m / s$ at an angle $3 0^{\circ}$ to the horizontal. At the same time a second particle $B$ is projected in opposite direction with initial speed of $50 m / s$ from a point at a distance of $100 m$ from $A$ . If the particles collide in air, find (a) the angle of projection $α$ of particle $B$ , (b) time when the collision takes place and (c) the distance of $P$ from $A$ , where collision occurs. $(g = 10 m / s^{2})$

Name: Video solution 1: A particle A is projected with an initial velocity of 60 m/s at an angle 30∘ to the horizontal. At the same time a second particle B is projected in opposite direction with initial speed of 50 m/s from a point at a distance of 100 m from A. If the particles collide in air, find (a) the angle of projection α of particle B, (b) time when the collision takes place and (c) the distance of P from A, where collision occurs. (g=10 m/s2)
Uploaded: 2023-03-24T05:28:00.000Z
Duration: 17 min

Views: 6,173 students

Updated on: Mar 24, 2023

Book:

Mechanics Volume 1 (DC Pandey)

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Michael Discussed

A particle

A

is projected with an initial velocity of

60 m / s

at an angle

3 0^{\circ}

to the horizontal. At the same time a second particle

B

is projected in opposite direction with initial speed of

50 m / s

from a point at a distance of

100 m

from

A

. If the particles collide in air, find (a) the angle of projection

α

of particle

B

, (b) time when the collision takes place and (c) the distance of

P

from

A

, where collision occurs.

(g = 10 m / s^{2})

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

(a) Taking

x

and

y

-directions as shown in figure.
Here,

a_{A} = - g \hat{j}

a_{B} = - g \hat{j}

u_{A x} = 60 cos 3 0^{\circ} = 303 m / s

u_{A y} = 60 sin 3 0^{\circ} = 30 m / s

u_{B x} = - 50 cos α

and

u_{B y} = 50 sin α

Relative acceleration between the two is zero as

a_{A} = a_{B}

. Hence, the relative motion between the two is uniform. It can be assumed that

B

is at rest and

A

is moving with

u_{A B}

. Hence, the two particles will collide, if

u_{A B}

is along

A B

. This is possible only when

u_{A y} = u_{B y}

i.e. component of relative velocity along

y

-axis should be zero.
or

30 = 50 sin α

∴

α = sin^{- 1} (3/5) = 3 7^{\circ}

(b) Now,

∣ u_{A B} ∣ = u_{A x} - u_{B x}

= (303 + 50 cos α) m / s

= (303 + 50 \times \frac{4}{5}) m / s

= (303 + 40) m / s

Therefore, time of collision is

t = \frac{A B}{∣ u _{A B} ∣} = \frac{100}{30 3 + 40}

t = 1.09 s

P

from

A

where collision takes place is

d = (u_{A x} t)^{2} + (u_{A y} t - \frac{1}{2} g t^{2})^{2}

= (303 \times 1.09)^{2} + (30 \times 1.09 - \frac{1}{2} \times 10 \times 1.09 \times 1.09)^{2}

d = 62.64 m

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Question Text	A particle $A$ is projected with an initial velocity of $60 m / s$ at an angle $3 0^{\circ}$ to the horizontal. At the same time a second particle $B$ is projected in opposite direction with initial speed of $50 m / s$ from a point at a distance of $100 m$ from $A$ . If the particles collide in air, find (a) the angle of projection $α$ of particle $B$ , (b) time when the collision takes place and (c) the distance of $P$ from $A$ , where collision occurs. $(g = 10 m / s^{2})$
Updated On	Mar 24, 2023
Topic	Motion in a Plane
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	229
Avg. Video Duration	21 min

Text solutionVerified

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