a projectile is fired vertically upwards and reaches a height of 0.0125 km find the velocity of projection and time takes it to reach its highest point
Answers
Answered by
0
Let a projectile is fired vertically upwards from the earth's surface with a velocity v and reaches a height h. Energy of the projectile at the surface of the earth is E
i
=
2
1
mv
2
−
R
E
GM
E
m
Energy of the projectile at a height h E
f
=−
R
E
+h
GM
E
m
(∴ At height h velocity of the projectile is zero.)
According to law of conservation of energy, E
i
=E
f
2
1
mv
2
−
R
E
GM
E
m
=−
R
E
+h
GM
E
m
2
1
mv
2
=GM
E
m[
R
E
1
−
R
E
+h
I
]=
(R
E
)(R
E
+h)
GM
E
mh
2
1
mv
2
=
R
E
+h
mghR
E
(∵g=
R
E
2
GM
E
)
As per question,
v=kv
e
=k
2gR
E
(∵v
e
=
2gR
E
)
and h=r−R
E
∴
2
1
mk
2
2gR
E
=
r
mg(r−R
E
)R
E
k
2
=
r
r−R
E
⇒(I−k
2
)r=R
E
⇒r=
1−k
2
R
E
Similar questions