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?
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?
To solve this problem, we can use the principle of conservation of momentum.
The initial momentum of the system (squid+water) is equal to the final momentum of the system.
Let's denote the initial velocity of the squid as V_squid and the initial velocity of the water as V_water. The mass of the squid is given as 0.60 kg and the mass of the expelled water is given as 0.30 kg. The velocity of the expelled water is given as 20 m/s.
The initial momentum of the system is the sum of the momenta of the squid and the water:
Initial momentum = (mass of the squid x initial velocity of the squid) + (mass of the water x initial velocity of the water)
Final momentum = (mass of the squid x final velocity of the squid) + (mass of the water x final velocity of the water)
Since the squid expels the water, the final velocity of the water is 0 (as it has detached from the squid).
Therefore, the initial momentum = final momentum
(mass of the squid x initial velocity of the squid) + (mass of the water x initial velocity of the water) = (mass of the squid x final velocity of the squid)
Substituting the known values:
(0.60 kg)(V_squid) + (0.30 kg)(20 m/s) = (0.60 kg)(final velocity of the squid)
Simplifying the equation:
0.60 kg x V_squid + 0.30 kg x 20 m/s = 0.60 kg x final velocity of the squid
0.60 kg x V_squid + 6 kg m/s = 0.60 kg x final velocity of the squid
Now, let's rearrange the equation to solve for the final velocity of the squid:
0.60 kg x final velocity of the squid = 0.60 kg x V_squid + 6 kg m/s
final velocity of the squid = (0.60 kg x V_squid + 6 kg m/s) / 0.60 kg
final velocity of the squid = V_squid + 10 m/s
Therefore, the speed of the squid immediately after expelling the water is equal to its initial velocity plus 10 m/s.
To find the speed of the squid immediately after expelling the water, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the squid and the expelled water form an isolated system.
The momentum before the expulsion can be calculated by multiplying the mass of the squid by its initial velocity. The momentum after the expulsion can be calculated by multiplying the mass of the squid (without the expelled water) by its final velocity. Since no external forces are acting on the system, the momentum before and after the expulsion must be equal.
Let's apply this principle to solve the problem:
Momentum before expulsion = Momentum after expulsion
(mass of squid) x (initial velocity of squid) = (mass of squid without water) x (final velocity of squid)
0.60 kg x (initial velocity of squid) = (0.60 kg - 0.30 kg) x (final velocity of squid)
0.60 kg x (initial velocity of squid) = 0.30 kg x (final velocity of squid)
Now we can solve for the final velocity of the squid:
(initial velocity of squid) = (0.30 kg x final velocity of squid) / 0.60 kg
(final velocity of squid) = [(initial velocity of squid) x 0.60 kg] / 0.30 kg
Given that the initial velocity of the water is 20 m/s, we can substitute this value into the equation:
(final velocity of squid) = [(20 m/s) x 0.60 kg] / 0.30 kg
(final velocity of squid) = (12 m/s) / 0.30 kg
(final velocity of squid) = 40 m/s
Therefore, the speed of the squid immediately after expelling the water is 40 m/s.