Answer:
a) The magnitude of the ball's velocity relative to Juan = 8.95 m/s
b) The direction of the ball's velocity relative to Juan is 24.1° from the +x-axis or N 65.9° E, that is, 65.9° east of North.
Explanation:
Relative velocity of a body X with respect to another body Y (Vₓᵧ) = velocity of Body X (Vₓ) - velocity of Body Y (Vᵧ)
Velocity of Juan in vector form = 7.6j m/s
Velocity of the ball in vector form = 13.9 [(sin 36°)î + (cos 36°)] (it has this form because the angle is given with respect to the y-axis, that is, N 36° E)
Velocity of the ball in vector form = (8.17î + 11.25j) m/s
a) The ball's velocity relative to Juan = (velocity of the ball) - (velocity of Juan) = (8.17î + 11.25j) - (7.6j) = (8.17î + 3.65j) m/s
Magnitude = √[(8.17)² + (3.65)²] = 8.95 m/s
b) direction of the ball relative to Juan = direction of the vector obtained in (a)
θ = Tan⁻¹ (3.65/8.17)
θ = 24.1°
