Question

a motorboat is to reach at a point 30 degree upstream with respect to normal on other side of a river flowing with velocity 5 metre per second velocity of motor boat with respect to water is 5 root 3 metre per second. the driver should steer the boat at an angle ​

Answer 1

Answer:

20.4°

Explanation:

a motorboat is to reach at a point 30 degree upstream with respect to normal on other side of a river flowing with velocity 5 metre per second velocity of motor boat with respect to water is 5 root 3 metre per second. the driver should steer the boat at an angle ​

Let Say Velocity = 5√3 m/s at angle α

Horizontal Velocity = 5√3Cosα

Net Horizontal Velocity = 5√3Cosα  - 5

Vertical Velocity = 5√3Sinα

As boat has to reach at 30°

=> tan 30  =  (5√3Sinα)/ (5√3Cosα  - 5 )

=> 1/√3 =  (5√3Sinα)/ (5√3Cosα  - 5 )

=> 5√3Cosα  - 5 = 15Sinα

=> √3Cosα - 1 = 3Sinα

=> √3Cosα - 3Sinα = 1

=> (Cosα(1/2) - √3Sinα/2) = 1/6

=> Sin30Cosα - Cos30Sinα = 1/6

=> Sin(30 - α) = 1/6

=> 30 - α = 9.6

=>  α = 20.4°

the driver should steer the boat at an angle ​ = 20.4°