Question

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?

Answer 1

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
<b>v1</b> = 19227 cos(90-120)<b>i</b> + 19227 sin(90-120)<b>j</b> = 16651.1<b>i</b> - 9613.5<b>j</b>

2.19 m/s * 35 min = 4599 m
<b>v2</b> = 4599cos(90-89)<b>i</b> + 4599sin(90-89)<b>j</b> = 4598.3<b>i</b> + 80.3<b>j</b>

<b>v1</b>+<b>v2</b> = 21249.4<b>i</b> - 9533.2<b>j</b>
= 23289.9m at 114.26°