A kid kicks a ball in such a way that the successive displacements of the ball are 6.00 m to the north, 4.50 m northest, 2.10 m at 30.0 degree west of south.

Find out the resultant displacement covered by the ball from starting point till ball becomes stationary again ?

Relevance

1st Kick: 6 m (N)

2nd Kick: 4.50 m (NE) => 4.50 x cos45* E & 4.50 x sin45* N = 3.18 m (N) & 3.18 m (E)

3rd Kick: 2.10 m (30* West of South) = 2.10 x cos30* (S) & 2.10 x sin30* (W) = 1.82 m (S) & 1.05 m (W)

Thus Final displacement from starting point = [6m (N) + 3.18m (N) + 1.82m (S)] & [3.18m (E) + 1.05m (W)]

=>Thus Final displacement from starting point = [7.36m (N)] & [2.13m (E)]

=>Thus Final displacement from starting point = √[(7.36)^2 + (2.13)^2] = 7.66m

& By tanθ = 2.13/7.36 = 0.29 = tan16.14*

=>θ = 16.14* from North towards East

• Displacement along north-south direction (north is positive)

= (6.00 + 4.50 cos45° - 2.10 cos30°) m

= 7.36 m

Displacement along east-west direction (east is positive)

= (4.5 sin45° - 2.1 sin30°) m

= 2.13 m

Magnitude of resultant displacement

= √(7.36² + 2.13²) m

= 7.66 m

tanθ = 2.13/7.36

θ = tan⁻¹(2.13/7.36)

θ = 16.1°

Direction of resultant displacement: N 16.1° E