Answer:
The magnitude of the velocity of boat w.r.t ground is 6.2015 m/s
Solution:
As per the question;
Width of the river, w = 216 m
Uniform speed of boat due east, [tex]u_{x} = 2.2\hat{i} m/s[/tex]
Angle in north west direction, [tex]\theta = 34^{\circ}[/tex]
Velocity of the boat relative to water, [tex]v_{bw} = 7.9m/s[/tex]
Now,
Velocity of the boat relative to the water is given by:
[tex]v_{bw} = -7.9cos34^{\circ}\hat{i} + 7.9sin34^{\circ}\hat{j}[/tex]
[tex]v_{bw} = - 6.55\hat{i} + 4.42\hat{j} m/s[/tex]
Also, velocity of water w.r.t ground is [tex]v_{wg} = u_{x} = 2.2\hat{i} m/s[/tex]
Now,
Magnitude of the velocity of boat w.r.t ground is given by:
[tex]v_{bg} = v_{bw} + v_{wg}[/tex]
[tex]v_{bg} = - 6.55\hat{i} + 4.42\hat{j} + 2.2\hat{i}[/tex]
[tex]v_{bg} = - 4.35\hat{i} + 4.42\hat{j} m/s[/tex]
[tex]|v_{bg}| = \sqrt{(- 4.35)^{2} + (4.42)^{2}} = 6.2015\ m/s[/tex]
