Answer:
(a) The speed is 7.96 m/s
(b) The direction is 76 degree from positive X axis in counter clockwise direction.
Explanation:
Width of river = 280 m
speed of river, vR = 4.7 m/s towards east
speed of boat with respect to water, v(B,R) = 7.1 m/s at 26 degree west of north
[tex]vR = 4.7 i \\\\v(B,R) = 7.1 (- sin 26 i + cos 26 j) = - 3.1 i + 6.4 j[/tex]
(a) The velocity of boat with respect to ground is
[tex]\overrightarrow{v}_{(B,R)}=\overrightarrow{v}_{(B,G)}-\overrightarrow{v}_{(R,G)}\\\\- 3.1 \widehat{i} +6.4 \widehat{j}=\overrightarrow{v}_{(B,G)} - 4.7 \widehat{i}\\\\\overrightarrow{v}_{(B,G)} = 1.6 \widehat{i} + 6.4 \widehat{j}\\\\{v}_{(B,G)} = \sqrt{1.6^2 + 6.4^2}=6.96 m/s[/tex]
(b) The direction is given by
[tex]tan\theta = \frac{6.4}{1.6} =4\\\\\theta = 76^o[/tex]
