A squid can propel itself by taking water into its body and then expelling it. A 0.60 kg squid expels 0.30 kg of water with a velocity of 20 m/s [S]. What is the speed of the squid immediately after expelling the water?
momentum is conserved ... Mw * Vw = Ms * Vs
the squid expels water equal to half of its own mass
so the squid's velocity will be half of the water's velocity
To find the speed of the squid immediately after expelling the water, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after the expulsion of water must be the same.
Let's denote the initial velocity of the squid as "v_squid_i" and the final velocity of the squid after expelling water as "v_squid_f". We are given the mass of the squid as 0.60 kg, the mass of the expelled water as 0.30 kg, and the velocity of the expelled water as 20 m/s.
The total momentum before the expulsion is the momentum of the squid alone, and after the expulsion, the momentum is the combined momentum of the squid and the expelled water. Since momentum is a vector quantity, we need to consider the directions as well.
Before the expulsion:
Momentum of squid = mass of squid * velocity of squid = 0.60 kg * v_squid_i
After the expulsion:
Momentum of squid and water = (mass of squid * final velocity of squid) + (mass of water * velocity of water)
= (0.60 kg * v_squid_f) + (0.30 kg * 20 m/s)
According to the principle of conservation of momentum, the total momentum before and after the expulsion should be equal:
0.60 kg * v_squid_i = (0.60 kg * v_squid_f) + (0.30 kg * 20 m/s)
Now we can solve this equation to find the final velocity of the squid (v_squid_f):
0.60 kg * v_squid_i - 0.60 kg * v_squid_f = 0.30 kg * 20 m/s
Rearranging the terms:
v_squid_f = (0.60 kg * v_squid_i - 0.30 kg * 20 m/s) / 0.60 kg
Plug in the values:
v_squid_f = (0.60 kg * v_squid_i - 0.30 kg * 20 m/s) / 0.60 kg
Solving this equation will give you the speed of the squid immediately after expelling the water.