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 30.0 degree east of south.
A)What is the magnitude of the velocity of the ball relative to the ground?

B) What is the direction of the velocity of the ball relative to the ground?
Answer in north of east please

Answer 1

Answer:

A. 2.83 m/s

B. 39.55 degrees north of east

Explanation:

The velocity of the ball relative to the ground is the sum vectors of velocity of the ball relative to Mia and the velocity of Mia relative to the ground

If we take north east as positive direction then

Velocity vector of the ball relative to Mia is

$= =$

Velocity of Mia relative to gorund is

<0, 5.3>

So velocity of the ball relative to the ground is

<1.8, -3.12> + <0, 5.3> = <1.8, 2.18>

Its magnitude is:

$v = \sqrt{v_e^2 + v_n^2} = \sqrt{1.8^2 + 2.18^2} = \sqrt{3.24 + 4.7524} = \sqrt{7.9924} = 2.83$  m/s

Its direction is

$tan\alpha = \frac{v_e}{v_n} = \frac{1.8}{2.18} = 0.83$

$\alpha = tan^{-1}0.83 = 0.69 rad \approx 39.55 degrees$  north of east