Question

I need solutions that are detailed for these introductory physics questions please!

Name: ID: 1. Consider a fish that swims toward and swallows a smaller fish. If the larger fish has a mass of 5kg and the smaller one has a mass of 1-kg fish, what is the velocity of the larger fish immediately after lunch if its velocity before lunch was 1 m/s to the right and if the smaller fish was moving to the left at a velocity of4m/s? 2. Marshall pushes crates starting from rest across the floorofhis classroom for 3s, with a net force as shown. Rank the following from greatest to least (justify your answers with brief calculations): 100 N 50 N 75 N 30 kg 20 kg 10 kg a) Impulses delivered b) Changes in momentum d) Final speeds

Answer 1

(1) Taking right as +ve while left as negative then initial momentum was

$m_1u_1+m_2u_2=5\times1+1\times(-4)=1$

Momentum after swallow of small fish wiill be

$(m_1+m_2)v$

By conservation of momentum

$(m_1+m_2)v=1\Rightarrow v=\frac{1}{m_1+m_2}=\frac{1}{5+1}=\frac{1}{6}$

(2)

$$Impulse: $ I_A=F_A\times t=100\times3=300\\ I_B=F_B\times t=75\times3=225\\ I_C=F_C\times t=50\times3=150\\$

(b) Change in momentum is same as impulse

(c) Final momentum is equal to impulse + initial momentum

$P_A=I_A+0=100\times3=300\\ P_B=I_B+0=75\times3=225\\ P_C=I_C+0=50\times3=150\\$

(d) Final speed is final momentum / mass