A sailboat is out on the water for a cruise. First it sails at a rate of 4.93 m/s, at an angle of 120.0° for a period of 65.0 minutes. The wind then shifts and the vessel makes progress at a rate of 2.19 m/s, at an angle of 85°, for a period of 35.0 minutes. What is the magnitude of the final displacement of the boat?
Since we're talking about sailing here, I assume by "angle" you mean a heading, with 0° being due North. If this is not what you mean, then make the appropriate adjustments.
4.93 m/s * 65 min = 19227 m
v1 = 19227 cos(90-120)i + 19227 sin(90-120)j = 16651.1i - 9613.5j
2.19 m/s * 35 min = 4599 m
v2 = 4599cos(90-89)i + 4599sin(90-89)j = 4598.3i + 80.3j
v1+v2 = 21249.4i - 9533.2j
= 23289.9m at 114.26°