A motor boat is racing towards north at 25 kmph and the water current in that region is 10 kmph in the direction of 60 degree east of south. find resultant velocity of the boat.
Answers
Answer:
The resultant velocity of the boat is 21.8 km/h.
Explanation:
Given that,
Speed of motorboat = 25 km/h
Speed of water current = 10 km/h
Angle = 60°
According to the figure,
The two velocities 25 km/h and 10 km/h are at angle 120°.
The magnitude of their resultant is,
R=\sqrt{A^2+B^2+2AB\cos\theta}R=
A
2
+B
2
+2ABcosθ
R=\sqrt{25^2+10^2+2\times25\times10\cos120^{\circ}}R=
25
2
+10
2
+2×25×10cos120
∘
R=\sqrt{25^2+10^2+2\times25\times10\times(-\dfrac{1}{2})}R=
25
2
+10
2
+2×25×10×(−
2
1
)
R = 21.8\ km/hR=21.8 km/h
Hence, The resultant velocity of the boat is 21.8 km/h.
Given,
Given,velocity of the water current vc
=10 km/s
=10 km/svelocity of the motorboat vb
=25km/h
=25km/hangle between north and south east =120 degree
resultant velocity=22km/h
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