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Maksim231197 [3]
2 years ago
9

In a World Cup soccer match, Juan is running due north toward the goal with a speed of 7.60 m/s relative to the ground. A teamma

te passes the ball to him. The ball has a speed of 12.9 m/s and is moving in a direction of 31.4° east of north, relative to the ground.a. What is the magnitude of the ball's velocity relative to Juan?b. What is the direction of the ball's velocity relative to Juan?
Physics
1 answer:
spayn [35]2 years ago
3 0

Answer:

Part a)

v_{bj} = 11.03 m/s

Part b)

\theta = 4.57 degree East of South

Explanation:

Part a)

Velocity of Juan is given as

v_1 = 7.60 m/s \hat j

velocity of the ball is given as

v_2 = 12.9(cos31.4 \hat i + sin31.4\hat j)

now we have

v_2 = 11\hat i + 6.72\hat j

Part a)

We need to find velocity of ball with respect to Juan

so it is given as

v_{bJ} = \vec v_b - \vec v_j

v_{bj} = 11\hat i + 6.72 \hat j - 7.6\hat j

v_{bj} = 11\hat i - 0.88\hat j

magnitude of the speed is given as

v_{bj} = \sqrt{11^2 + 0.88^2}

v_{bj} = 11.03 m/s

Part b)

direction of velocity of the ball

tan\theta = \frac{v_y}{v_x}

tan\theta = \frac{-0.88}{11}

\theta = 4.57 degree East of South

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