Answer:
vf = 14.2176 m/s
Explanation:
Given
m = 4 Kg
viy = 7.00 ĵ m/s
Fx = 11.0 î N
t = 4.5 s
vf = ?
Using the Impulse - Momentum Theorem, we have
F*Δt = m*Δv   ⇒  F*Δt = m*(vf - vi)
⇒   vf = (F*Δt + m*vi) / m
⇒   vf = (F*Δt + m*vi) / m
For x-component
⇒   vfx = (Fx*Δt + m*vix) / m = (11 N*4.5 s + 4 Kg*0 m/s) / (4 Kg)
⇒   vfx = 12.375 î m/s
For y-component
⇒   vfy = (Fy*Δt + m*viy) / m = (0 N*4.5 s + 4 Kg*7 m/s) / (4 Kg)
⇒   vfy = 7 ĵ m/s
Finally:
vf = √(vfx² + vfy²)
⇒  vf = √((12.375 m/s)² + (7 m/s)²)
⇒  vf = 14.2176 m/s