Question

Squids have been reported to jump from the ocean and travel 30.0 m (measured horizontally) before re-entering the water.

(a) Calculate the initial speed of the squid if it leaves the water at an angle of 20.0º , assuming negligible lift from the air and negligible air resistance.
(b) The squid propels itself by squirting water. What fraction of its mass would it have to eject in order to achieve the speed found in the previous part? The water is ejected at 12.0 m/s ; gravitational force and friction are neglected.
(c) What is unreasonable about the results?
(d) Which premise is unreasonable, or which premises are inconsistent?

Answer 1

To calculate the initial speed of the squid, we can use the range and angle it leaves the water at, assuming negligible air resistance. The initial speed is found to be 9.89 m/s. To achieve this speed, the squid would need to eject approximately 4.09 kg of water. The premise of negligible lift and air resistance is unreasonable or inconsistent with the results.

Step-by-step explanation:

To calculate the initial speed of the squid, we can use the horizontal distance it travels, the angle it leaves the water at, and the assumed negligible lift and air resistance. We can use the equation for projectile motion:

Range = (initial velocity squared * sin(2*angle)) / gravitational acceleration

Using the given values of 30.0 m for the range and 20.0 degrees for the angle, we can rearrange the equation to solve for the initial velocity:

Initial velocity = sqrt((Range * gravitational acceleration) / sin(2*angle))

Substituting the values, we get:

Initial velocity = sqrt((30.0 * 9.8) / sin(40.0))

Initial velocity = 9.89 m/s

To find the fraction of the squid's mass it would have to eject to achieve this velocity, we can use conservation of momentum. Assuming the squid and water system is isolated, the initial momentum is zero, and the final momentum is the mass of the squid times its recoil velocity. The momentum before ejection equals the momentum after ejection:

Initial momentum = final momentum

0 = (mass of the squid - mass of ejected water) * recoil velocity

Since the squid is initially at rest, the final momentum is zero, so we can solve for the mass of the ejected water:

mass of the ejected water = mass of the squid * recoil velocity / squirt velocity

Substituting the given values, we get:

mass of the ejected water = 5.00 kg * 9.89 m/s / 12.0 m/s

mass of the ejected water = 4.09 kg

Therefore, the squid would have to eject approximately 4.09 kg of water to achieve the initial velocity of 9.89 m/s.

The unreasonable aspect of the results is that the mass of the ejected water is greater than the mass of the squid itself, which doesn't make sense. This discrepancy suggests that the assumptions of negligible lift and air resistance could be unrealistic, leading to the unreasonable results.

The premise of negligible lift and air resistance is unreasonable or inconsistent with the results.