Two stones are thrown vertically upward stimutaneously with their initial velocities u1 and u2 respectively. Prove that the heights reached by them would be in the ratio of u 2221 :u ( assume that upward acceleration is -g and downward acceleration is +g .
Please answer this with step by step explanation.
Science class 9th chapter motion
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Answer:
Given, initial velocities: u₁ and u₂
g=acceleration due to gravity, here it is (-g), as the object is thrown vertically upwards
Let Final velocities: v₁ and v₂
Now, we know that,
s= \frac{v^2-u^2}{2g}s=
2g
v
2
−u
2
For object 1:
s_1= \frac{v_1^2-u_1^2}{-2g}s
1
=
−2g
v
1
2
−u
1
2
Putting v=0
s_1= \frac{-u_1^2}{-2g}= \frac{u_1^2}{2g}s
1
=
−2g
−u
1
2
=
2g
u
1
2
..................(i)
Similarly for object 2:
s_2= \frac{u_2^2}{2g}s
2
=
2g
u
2
2
......................(ii)
Divide (i) by (ii)
\frac{s_1}{s_2} = \frac{ (\frac{u_1^2}{2g} )}{ (\frac{u_2^2}{2g}) }
s
2
s
1
=
(
2g
u
2
2
)
(
2g
u
1
2
)
Therefore,
\frac{s_1}{s_2}= \frac{u_1^2}{u_2^2} \ or \ u_1^2:u_2^2
s
2
s
1
=
u
2
2
u
1
2
or u
1
2
:u
2
2
Hence Proved
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