You are stranded in the middle of a frozen pond, 788 m in diameter which is so slippery that your feet slide freely and don't move you. In desperation you write an S.O.S. on your hat, mass 0.4 kg, and fling it towards the north with a velocity of 11 m/s at 51 o with the horizontal. If your mass is 63 kg, how long does it take you to reach the shore? (in hours)

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aristocles aristocles · Answer 1 · 2019-11-07T02:25:18+01:00

Answer:

[tex]t = 2.48 hour[/tex]

Explanation:

As we know that hat is thrown off by speed 11 m/s at an angle of 51 degree with the horizontal

so we will have

[tex]v_x = 11 cos51= 6.92 m/s[/tex]

[tex]v_y = 11 sin51 = 8.55 m/s[/tex]

now we know that in x direction there is no eternal force on it

so we will have by momentum conservation

[tex]M_1v_1 + m_2v_2 = 0[/tex]

[tex]63 v_1 + 0.4(6.92) = 0[/tex]

so we have

[tex]v_1 = 0.044 m/s[/tex]

Now we know that the time to reach the opposite end is given as

[tex]t = \frac{R}{v}[/tex]

[tex]t = \frac{394}{0.044}[/tex]

[tex]t = 8954.5 s[/tex]

[tex]t = 2.48 hour[/tex]