Question

A 748-N man stands in the middle of a frozen pond of radius 4.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics textbook horizontally toward the north shore at a speed of 4.0 m/s. How long does it take him to reach the south shore

Answer 1

The man will take 64 seconds to reach to the south shore of the frozen pond.

Explanation:

Given:

Weight of the man = 748 N Mass of the man,
`(m)= (W)/(g)` =
`(748)/(9.8)` =
`76.32` kg

Radius of the pond
`(r)` = 4 m

Mass of the textbook = 1.2 kg

Velocity at which the textbook is thrown = 4 ms^1

We have to find the velocity of the man after the throw.

Let the velocity is
`V_m` .

Now using law of conservation of momentum we can find the
`V_m` value.

`m_(_b_)V_b_(_i_) +m_(_m_)V_m_(_i_) =m_(_b_)V_b_(_f_)+m_(_m_) V_m_(_f_)`

Considering
`V_m_(_f_)=V_m`

And initial velocity of both the man and book i.e
`V_b_(_i_)=0,\ V_m_(i_)=0`

So,

⇒
`0 =m_(_b_)V_b_(_f_)+m_(_m_) V_m`

⇒ Plugging the values.

⇒
`V_m=-(m_(_b_)V_b_(_f_))/(m_(_m_))`

⇒
`V_m=-(1.2* 4)/(76.32)`

⇒
`V_m=-0.062` ms^-1

Here the negative velocity is meant for opposite direction of the throw.

Numerically we will write,
`V_m = 0.062`

With this velocity the man will move towards south.

We have to calculate the time taken by the man to move to its south shore.

And we know
`velocity(v)* time(t) = distance(d)`

Let the time taken be
`t` and
`v* t = d` and
`d=r` then,
`V_m* t=r`

Then

⇒
`t=(radius\ (r))/(V_m)`

⇒ Plugging the values.

⇒
`t=(4)/(0.062)`

⇒
`t =64` sec

The man will take 64 seconds to reach to the south shore of the frozen pond (circular).