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

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

Step-by-step explanation:

Given:

Weight of the man = 748 N      Mass of the man, = = kg

Radius of the pond = 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 .

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

Considering

And initial velocity of both the man and book i.e

So,

⇒

⇒ Plugging the values.

⇒

⇒

⇒ ms^-1

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

Numerically we will write,

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

Let the time taken be and and then,

Then

⇒

⇒ Plugging the values.

⇒

⇒ sec

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

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1