Respuesta :
Answer:
a. The magnitude of the resultant velocity vector of the fish is approximately 5.83 m/s
The direction of the resultant velocity vector of the fish is approximately 30.93° relative to the direction of the river
b. The magnitude of the resultant velocity vector of the surfer is approximately 6.083 m/s
The direction of the resultant velocity vector of the surfer is approximately 9.46° relative to the direction of the wave
Explanation:
a. The given parameters of the fish and the river are;
The speed with which the fish is swimming across the river, v₁ = 3.0 m/s
The velocity with which the river is flowing, v₂ = 5.0 m/s
Therefore, in vector form, we have;
v₁ = 3.0·j
v₂ = 5.0·i
The resultant velocity, R = v₁ + v₂ = 5.0·i + 3.0·j
∴ R = 5.0·i + 3.0·j
The magnitude of the resultant velocity vector, [tex]\left | R \right |[/tex] = √(5.0² + 3.0²) =√34 ≈ 5.83
The magnitude of the resultant velocity vector, of the fish, [tex]\left | R \right |[/tex] ≈ 5.83 m/s
The direction of the resultant velocity of the fish, θ = arctan(3.0/5.0) ≈ 30.93°
Therefore, The direction of the resultant velocity vector of the fish, θ ≈ 30.93° relative to the direction of the river
b. The given parameters of the surfer and the wave are;
The speed with which the surfer is travelling, v₁ = 1.0 m/s
The speed of the wave travelling across, v₂ = 6.0 m/s
Therefore, in vector form, we have;
v₁ = 1.0·j
v₂ = 6.0·i
The resultant velocity, R = v₁ + v₂ = 1.0·i + 6.0·j
∴ R = 1.0·i + 6.0·j
The magnitude of the resultant velocity of the surfer, [tex]\left | R \right |[/tex] = √(1.0² + 6.0²) =√37 ≈ 6.083
The magnitude of the resultant velocity vector of the surfer, [tex]\left | R \right |[/tex] ≈ 6.083 m/s
The direction of the resultant velocity of the surfer, θ = arctan(1.0/6.0) ≈ 9.46°
Therefore, The direction of the resultant velocity vector of the surfer, θ ≈ 9.46° relative to the direction of the wave
