The correct option is
D Time interval between firings is
0.4 sGiven, speed of shots
=5 m/s
Height of hill
=15 m
Angle of fire of one shot
=45∘ with horizontal
Angle of fire of other shot
=0∘ with horizontal
We know that, equation of trajectory of projectile is given by,
Y=X tanθ−gX22u2cos2θ
[origin of co- ordinate system for this equation is at point of projection]
For shot 1,
Y=X×1−10X22×52×12
Y=X−2X25−−−−(1)
Similarly, of shot 2
Y=X×0−10X22×52×1
Y=−X25−−−−(2)
As both shots collide in air at a point P then its x and y co-ordinates should be same.
From (1) and (2)
X−2X25=−X25
⇒X−X25=0
⇒X(1−X5)=0
⇒X=0 and
X=5 ----(3)
on putting (3) in (2)
Y=−5
Therefore, with respect to original coordinate system with origin at bottom of the tower,
co - ordinates of P is
x=5 m and
y=10 m
Time taken by shot fired at
45∘ with horizontal to reach point
P, is t1=55cos45∘=√2=1.4 s [Horizontal motion]
Time taken by shot fired at horizontal to reach point
P, is t2=55=1 s [Horizontal Motion]
∴ Time internal between firings for collision to happen is
=t1−t2=1.4−1=0.4 s