Car A is moving towards 37 degrees WN with speed 10 m/s.Driver of car A sees that another B moving towards 53 degrees EN.speed of car B is 10√5 m/s.find relative velocity V B/A, and direction of car B?

Question

Answer

Problem Statement:

Car A is moving towards 37 degrees WN with speed 10 m/s. Driver of car A sees that another B moving towards 53 degrees EN. Speed of car B is 10√5 m/s. Find relative velocity V B/A and direction of car B?

Solution:

Relative Velocity:

Relative velocity is the velocity of an object in relation to another moving object.

Relative velocity can be calculated using the vector subtraction method, which involves subtracting the velocity of one object from the velocity of the other object.

Calculating Velocity V_A:

Since the speed of car A is given as 10 m/s and its direction is 37 degrees WN, we can find the velocity vector of car A using the following formula:

V_A = 10(cos(37)i - sin(37)j)

V_A = 8i - 6j

Calculating Velocity V_B:

Since the speed of car B is given as 10√5 m/s and its direction is 53 degrees EN, we can find the velocity vector of car B using the following formula:

V_B = 10√5(cos(53)i + sin(53)j)

V_B = 5(4i + 3j)

V_B = 20i + 15j

Calculating Relative Velocity:

The relative velocity of car B with respect to car A can be calculated by subtracting V_A from V_B.

V_B/A = V_B - V_A

V_B/A = (20i + 15j) - (8i - 6j)

V_B/A = 12i + 21j

Direction of Car B:

The direction of car B can be calculated using the following formula:

θ = tan^-1(V_B/Ay/V_B/Ax)

θ = tan^-1(21/12)

θ = 59.04 degrees

Therefore, the direction of car B is 59.04 degrees from the negative x-axis.

Conclusion:

The relative velocity of car B with respect to car A is 12i + 21j m/s and the direction of car B is 59.04 degrees from the negative x-axis.

Answer

VB/A=14(√5-1) in the E-S direction.

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