Question

Two particles are projected from the same point on the ground, with same speed simultaneously at angles alpha and beta with the horizontal. They strike the ground at same point after times t1 and t2, respectively. Then:

Answer 1

Answer:

ANSWER

A B

θ=αθ=β

R=RR=R

H=h

1

H=h

2

u=uu=u

t

1

=

g

2usinα

t

2

=

g

2usinβ

t

2

t

1

=

g

2usinα

⋅

2usinβ

g

=

sin(π/2−α)

sinα

=tanα (Option C)

R

1

=

g

u

2

sin2α

R

2

=

g

u

2

sin2β

∵R

1

=R

2

⇒sin2α=sin2β

⇒2α=π−2β

⇒α+β=π/2 (Option A)

H

1

=

2g

u

2

sin

2

α

H

2

=

2g

u

2

sin

2

β

H

2

H

1

=(

2g

u

2

sin

2

α

⋅

u

2

sin

2

β

2g

)

1/2

H

2

H

1

=

sinβ

sinα

=

sin(π/2−α)

sinα

=tanα (Option D)

H

1

H

2

=

2g

u

2

sinαsinβ

=

4g

2u

2

sinαsin(π/2−α)

H

1

H

2

=

4g

u

2

sin2α

4

H

1

H

2

=R (Option B)

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