Question

Squids are the fastest marine invertebrates, using a powerful set of muscles to take in and then eject water in a form of jet propulsion that can propel them to speeds of over 11.5 m/s. What speed (in m/s) would a stationary 1.60 kg squid achieve by ejecting 0.115 kg of water (not included in the squid's mass) at 3.50 m/s? Neglect other forces, including the drag force on the squid. HINT m/s

Answer 1

Answer:

0.25 m/s

Explanation:

This problem can be solved by using the law of conservation of momentum - the total momentum of the squid-water system must be conserved.

Initially, the squid and the water are at rest, so the total momentum is zero:

$p_i = 0$

After the squid ejects the water, the total momentum is

$p_f = m_s v_s + m_w v_w$

where

$m_s = 1.60 kg$ is the mass of the squid

$v_s$ is the velocity of the squid

$m_2 = 0.115 kg$ is the mass of the water

$v_w = 3.50 m/s$ is the velocity of the water

Due to the conservation of momentum,

$p_i = p_f$

so

$0=m_s v_s + m_w v_w$

so we can find the final velocity of the squid:

$v_s = -\frac{m_w v_w}{m_s}=-\frac{(0.115 kg)(3.50 m/s)}{1.60 kg}=-0.25 m/s$

and the negative sign means the direction is opposite to that of the water.