Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia.

Question

Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 7.00 m/s . The velocity of the ball relative to Mia is 4.20 m/s in a direction 30.0 east of south.

Part A

What is the magnitude of the velocity of the ball relative to the ground?
Express your answer to three significant figures and include the appropriate units.

Part B

What is the direction of the velocity of the ball relative to the ground?

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Here,

velocity of Mia , vm = 7 j m/s

vcelocity of ball relative to the ground , vbm = 4.20 * (sin(30) i - * cos(30) j)

vbm = 2.1 i - 3.64 j m/s

for the velocity of ball relative to ground vb
vbm = vb - vm

vb = vbm + vm

vb = 7 j + 2.1 i - 3.64 j

vb = 2 i + 3.36 j m/s

magnitude of the velocity = sqrt(2^2 + 3.36^2)

magnitude of the velocity = 3.91 m/s

the magnitude of velocity is 3.91 m/s

b) direction of ball's velocity = arctan(3.36/2) degree north of east

direction of ball's velocity = 59.2 degree north of east

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