Question

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are: - 4.0 m north - 2.0 m northeast - 1.0 m at 30◦ to the west of south starting at the same initial point, an expert golfer could make the hole in what single displacement?

Answer 1

its displacement is given in vector form as follows

$\vec d_1= 4 \hat j$

$\vec d_2 = 2 cos45 \hat i + 2 sin45 \hat j$

$\vec d_2 = 1.41 \hat i + 1.41 \hat j$

$\vec d_3 = -1 sin30 \hat i - 1 cos30 \hat j$

$\vec d_3 = -0.5 \hat i - 0.866 \hat j$

now the total displacement due to all three is given as

$d = d_1 + d_2 + d_3$

$d = (1.41 - 0.5)\hat i + (4 + 1.41 -0.866)\hat j$

$d = 0.91 \hat i + 4.54 \hat j$

so magnitude of displacement is

$d = \sqrt{0.91^2 + 4.54^2} = 4.63 m$

direction is given as

$\theta = tan^{-1}\frac{4.54}{0.91}$

$\theta = 78.7 degree$

so the ball will be displaced by 4.63 m at angle 78.7 degree North of East