ANSWER-
Let's start by finding the momentum of the predator fish before the collision. We can use the formula:
p1 = m1 * v1
where p1 is the momentum of the predator fish, m1 is its mass, and v1 is its velocity. Substituting the given values, we get:
p1 = 11 kg * 75.0 cm/s
p1 = 825 kg·cm/s
Next, let's find the momentum of the small fish before the collision. Again, we can use the formula:
p2 = m2 * v2
where p2 is the momentum of the small fish, m2 is its mass, and v2 is its velocity. Substituting the given values, we get:
p2 = 1.2 kg * 36.0 cm/s
p2 = 43.2 kg·cm/s
The total momentum before the collision is the sum of p1 and p2:
p = p1 + p2
p = 825 kg·cm/s + 43.2 kg·cm/s
p = 868.2 kg·cm/s
After the collision, the predator fish and the small fish move together as one object. Let's assume that their combined mass is M, and their combined velocity is v. Then, the total momentum after the collision is:
p' = M * v
According to the law of conservation of momentum, p' must be equal to p:
p' = p
M * v = 868.2 kg·cm/s
To solve for v, we need to find M. The combined mass of the predator fish and the small fish is:
M = m1 + m2
M = 11 kg + 1.2 kg
M = 12.2 kg
Substituting this value into the equation for p', we get:
12.2 kg * v = 868.2 kg·cm/s
v = 71.1 cm/s
The magnitude of the velocity of the predator fish after swallowing the small fish is 71.1 cm/s. To find the direction, we can use the concept of vector addition. The velocity of the predator fish before the collision is purely in the eastward direction, so we can represent it as a vector:
v1 = 75.0 cm/s east
The velocity of the small fish before the collision is purely in the southward direction, so we can represent it as a vector:
v2 = 36.0 cm/s south
The velocity of the predator fish and the small fish after the collision can be represented as a vector sum of v1 and v2:
v = v1 + v2
To find the direction of v, we can use the tangent function:
θ = tan⁻¹(v2 / v1)
θ = tan⁻¹(36.0 cm/s / 75.0 cm/s)
θ = 26.6° south of east
Therefore, the direction of the velocity of the predator fish after swallowing the small fish is 26.6° south of east.