Question

Example 33 Two guns situated at the top
height 10 m fire one shot each with the same speed 53 m/s
at some interval of time. One gun fresh and the
other fires upwards at an angle of 60" with the horizontal
The two shots collide in air at a point in time tena
between the firing and (ii) the coordinates of the peoP
Take the origin of coordinates system the foot of the hill
right below the muzzle and trajectories in the plane​

Answer 1

Explanation:

ANSWER

Let gun 1 fire at t=0sec and gun 2 fire at t=ssec After tsec

For gun 1

V

x

=5

3

m/sa

x

⇒x

1

=5

3

t

V

y

=0,a

y

=−g⇒y

1

=0−

2

1

gt

2

For gun 2

V

x

=5

3

cos60°,a

x

=0⇒x

2

=5

3

cos60°(t

−

t

1

)

V

y

=5

3

sin60°,a

x

=−g⇒y

2

=5

3

sin60°(t−t

1

)−

2

1

g(t−t

1

)

2

At collison x

1

=x

2

&y

1

=y

2

⇒5

3

t=5

3

2

1

(t−t

1

)

⇒5

3

t=

2

5

3

t

−5

3

t

1

&−5t

2

=

2

5

3

.

3

(t−t

1

)−5(t−t

1

)

2

Solving we get t

1

=−1sec&t=1sec

∵t

1

is negative

Gun 2 fires before gun1

Now, x=5

3

t=5

3

y=−

2

1

gt

2

=−5

∴ Collison point P=(5

3

,−5)