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 5.30 m/s. The velocity of the ball relative to Mia is 3.60 m/s in a direction 30.0degree east of south.

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.

B)
What is the direction of the velocity of the ball relative to the ground ( North of East) ?
Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Given data Velocity of Mia relative to ground due north is, VMg = 5.30 m/s (j) Velocity of the ball relative to Mia is, VbM = 3.60 m/s cos 30o (-j) +  3.60 m/s sin 30o (i)                                                               = 3.1176 (- j) + 1.8 (i) A) Velocity of the ball relative to the ground is,                               Vbg = VbM + VMg                                      = 5.3 (j) + 3.1176 (-j ) + 1.8 (i) Then the x component of  Vbg,x = 1.8 (i) And y component of  Vbg,y = 5.3 (j) + 3.1176 (-j )                                             = 2.18 (j) Magnitude of the velocity of the ball relative to the ground is,                                     Vbg = (1.8)2 + (2.18)2                                              = 2.8 m/s ----------------------------------------------------------------------------------------------------- B) Direction of the velocity of the ball relative to the ground is,                                         = tan-1 ( 2.18 m/s / 1.8 m/s )                                             = 50.45o                                                                           = 5.3 (j) + 3.1176 (-j ) + 1.8 (i) Then the x component of  Vbg,x = 1.8 (i) And y component of  Vbg,y = 5.3 (j) + 3.1176 (-j )                                             = 2.18 (j) Magnitude of the velocity of the ball relative to the ground is,                                     Vbg = (1.8)2 + (2.18)2                                              = 2.8 m/s ----------------------------------------------------------------------------------------------------- B) Direction of the velocity of the ball relative to the ground is,                                         = tan-1 ( 2.18 m/s / 1.8 m/s )                                             = 50.45o                                                                          

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