Answer:
Question 1:
[tex]\vec V=-32.6mph\cdot \hat i+33.8mph\cdot \hat j[/tex]
Question 2:
[tex]\vec V_b=52.6mph\hat i-33.0mph\hat j[/tex]
Explanation:
1. Balloon moving at 47 mph on a bearing of 134º
The x-component of a vector is the magnitude of the vector multiplied by the cosine of the angle.
The y-component of a vector is the magnitufe of the vector multiplied by the sine of the angle.
[tex]\vec V=47mph\cdot cos(134\º)\hat i+47mph\cdot sin(134\º)\hat j[/tex]
[tex]\vec V=-32.6mph\cdot \hat i+33.8mph\cdot \hat j[/tex]
2. Balloon moving at 51mph on a bearing of 341º, with a wind blowing at 17mph on a bearing of 285º
First find, the component forms of the initial velocity of the balloon and of the wind. Then, add the two velocities.
i) Initial velocity of the balloon: Vb,i
[tex]\vec V_{b,i}=51mph\cdot cos(341\º) \hat i+51mph\cdot sin(341\º)\hat j[/tex]
[tex]\vec V_{b,i}=48.2mph\cdot \hat i-16.6mph\cdot \hat j[/tex]
ii) Wind velocity: Vw
[tex]\vec V_w=17mph\cdot cos(285\º)\hat i+17mph\cdot sin(285\º)\hat j[/tex]
[tex]\vec V_w=4.4mph\cdot \hat i-16.4mph\cdot \hat j[/tex]
iii) Add the two velocities
Add the corresponding components:
[tex]\vec V_b=(48.2mph+4.4mph)\cdot \hat i+(-16.6mph-16.4mph)\cdot \hat j[/tex]
[tex]\vec V_b=52.6mph\hat i-33.0mph\hat j[/tex]
