Question

A(n) 681 N man stands in the middle of a frozen pond of radius 12.3 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 1.3 kg physics textbook horizontally toward the north shore, at a speed of 6 m/s. The acceleration of gravity is 9.81 m/s 2 . How long does it take him to reach the south shore? Answer in units of s.

Answer 1

It takes him 109.47 seconds to reach the south shore.

Step-by-step explanation:

Due to conservation of linear momentum when the man throws his textbook horizontally, he's going to move in the opposite direction, because there are not dissipative forces as friction. So, the change on linear momentum must be zero:

`\varDelta\overrightarrow{p}=0` that implies
`p_(M)=p_(m)` (M for man and m for textbook)

`MV_(M)=mV_(m)`

with m the mass of the textbook,
`V_(m)` textbook velocity, M the mass of the man (that is
`(681)/(9.81)=69.42\,kg`) and
`V_M` his velocity after he throws the book. Solving (1) for
`V_M`:

`V_(M)=(mV_(m))/(M)=((1.3)(6))/((69.42))`

`V_(M)=0.11\, (m)/(s)`

Now, because there's no friction between his shoes and the ice, the man is going to move with constant velocity, and we should find in how much time is going to reach the south shore with the kinematic equation:

`t=(distance)/(V_(M))=(12.3)/(0.11)}`

`t=109.47\,s`