A stone is projected horizontally with 20m/s and it hits the vertically wall in front of stone at a distance of 60m. Taking projection point of stone as a origin of x-y plane find the co-ordinates of point of hit on the vertical wall:
Answers
Let u is the initial velocity
Maximum height H=
2g
u
2
sin
2
θ
=2h
h=
4g
u
2
sin
2
θ
Horizontal component of the velocity u
x
=ucosθ
Vertical component u
y
=usinθ
At maximum height
v
y
2
−u
y
2
=−2g(2h)
u
y
=usinθ=2
gh
t be the time taken by the stone to attain the vertical height h
h=u
y
t−
2
1
gt
2
t
2
−(
g
2u
y
)t+
g
2h
=0
t=(4±
2
)
g
h
t
1
=(4−
2
)
g
h
t
2
=(4+
2
)
g
h
So bird travel horizontal distance from initial position to final position = AB in time t
2
velocity of the bird=v
b
AB=v
b
t
2
Same distance AB traveled by the stone in time t
2
−t
1
AB=u
x
(t
2
−t
1
)
u
x
v
b
=
t
2
(t
2
−t
1
)
=
(4+
2
)
g
h
)
((4+
2
)
g
h
)−((4−
2
)
g
h
)
=
(
2
+1)
2
Answer: