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.**

A golfer takes three strokes to putt a golf ball into a hole. On
the first stroke, the ball moves 4.4 m due east. On the second, it
moves 2.2 m at an angle 20° north of east. On the third, it moves
0.50 m due north. If the golfer had instead hit the ball directly
into the hole on the first stroke, what would have been the
magnitude (in m) and direction of the ball's displacement? Give the
direction...

A golfer, putting on a green, requires three strokes to “hole
the ball.” During the first putt, the ball rolls 5.0 m due east.
For the second putt, the ball travels 2.1 m at an angle of 20.0
north of east. The third putt is 0.50 m due north. What
displacement (magnitude and direction relative to due east) would
have been needed to “hole the ball” on the very first putt?

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