A 5-kg fish swimming 1 m/s swallows an absent minded 1-kg fish swimming toward it at a speed that brings both fish to a halt immediately after lunch. Show that the speed of the approaching smaller fish before lunch must have been 5 m/s.

Question

07-10-2019
Physics

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A 5-kg fish swimming 1 m/s swallows an absent minded 1-kg fish swimming toward it at a speed that brings both fish to a halt immediately after lunch. Show that the speed of the approaching smaller fish before lunch must have been 5 m/s.

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AMB000 AMB000 · Answer 1 · 2019-10-09T20:42:34+02:00

Answer:

[tex]v_2=-5m/s[/tex]

Explanation:

If we call the big fish as 1 and the small one as 2 we write their initial linear momentum as:

[tex]p_i=m_1v_1+m_2v_2[/tex]

While their final linear momentum will be (since both are together we call their final velocity v):

[tex]p_f=m_1v+m_2v=(m_1+m_2)v[/tex]

But their final velocity is 0, so [tex]p_f=0[/tex], and since linear momentum must be conserved we have [tex]p_i=p_f=0[/tex], which means:

[tex]m_1v_1+m_2v_2=0[/tex]

We want the speed of the approaching smaller fish ([tex]v_2[/tex]), so:

[tex]m_1v_1=-m_2v_2[/tex]

[tex]v_2=-\frac{m_1v_1}{m_2}[/tex]

And just substitute our values:

[tex]v_2=-\frac{(5Kg)(1m/s)}{1Kg}=-5m/s[/tex]

Where the minus sign indicates that the small fish goes in the opposite direction as the big fish.

alokdubeyvidyaatech alokdubeyvidyaatech · Answer 2 · 2022-02-16T15:24:47+01:00

The speed of small fish is found out by linear momentum which is conserved before and after lunch.

The speed of small fish before lunch is 5 m/s.

What is the speed?

The speed of an object can be defined as the total distance covered by the object in a given time interval.

Given that the speed v1 of big fish is 1 m/s and mass m1 is 5 kg. The mass m2 of small fish is 1 kg.

The linear momentum of both the fish is given as,

[tex]p_1=m_1v_1 + m_2v_2[/tex]

Where p1 is the initial linear momentum and v2 is the speed of the small fish.

Both the fish are moving towards each other, so if v is the common velocity of both fish after meeting, then the final linear momentum will be given as,

[tex]p_2 = (m_1+m_2)v[/tex]

The linear momentum is conserved hence,

[tex]p_1 = p_2[/tex]

[tex]m_1v_1 + m_2v_2 = (m_1+m_2)v[/tex]

The final velocity of fish will be zero because they took a halt, so

[tex]m_1v_1 + m_2v_2 = 0[/tex]

[tex]v_2 = -\dfrac {m_1v_1}{m_2}[/tex]

[tex]v_2 = - \dfrac {5\times 1}{1}[/tex]

[tex]v_2 = -5\;\rm m/s[/tex]

The negative sign shows that the small fish moving in the opposite direction.

Hence we can conclude that the speed of small fish before lunch is 5 m/s.

To know more about speed and momentum, follow the link given below.

https://brainly.com/question/5794232.