Question

A novice golfer can shoot the ball in three strokes in the following direction: 4m due east, 7m due north, and lastly, 5m, θ° = tan ^-1 (3/4) north of east.

An expert golfer on the other hand, can shoot the ball in just one stroke. What are the x and y components of the displacement made by the expert golfer?

A. 3m and 10m

B. 5m and 10m

C. 6m and 12m

D. 8m and 10m

**Without a calculator, how can we solve the problem?

Answer 1

Net displacement is given by: (wrong answer)

d = d1 + d2 + d3

d1 = 4 m due east = 4*cos 0 deg i + 4*sin 0 deg j

d1 = 4 i + 0 j

d2 = 7 m due north = 7*cos 90 deg i + 7*sin 90 deg j

d2 = 0 i + 7 j

d3 = 5 m at = arctan (3/4) deg north of east, So

sin = 3/5, and cos = 4/5 (from right-angle triangle properties)

d3 = 5*cos i + 5*sin j = 5*(4/5) i + 5*(3/5) j

d3 = 4 i + 3 j

Net displacement will be

d = d1 + d2 + d3

d = (4 + 0 + 4) i + (0 + 7 + 3) j

d = 8 i + 10 j

x-component = 8 m and y component = 10 m

Correct option is D.