Question

If a body loses half of it's velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest.?

Answer 1

Explanation:

Let initial velocity be v.

Initial Energy =

2

1

mv

2

Final energy =

2

1

m(

2

v

)

2

=

4

1

(

2

1

mv

2

)

Energy lost =

2

1

mv

2

−

4

1

(

2

1

mv

2

)=

4

3

(

2

1

mv

2

),−−−−−−(for 3 cm)

So, Remaining energy =

4

1

(

2

1

mv

2

)

Using unitary method,

4

3

(

2

1

mv

2

)→3 cm penetration

⇒

4

1

(

2

1

mv

2

)→1 cm penetration