Question

The 18th hole at Pebble Beach Golf Course is a dogleg to the left of length 496.0 m. The fairway off the tee is taken to be the x direction. A golfer hits his tee shot a distance of 300.0 m, corresponding to a displacement Δ→r1=300.0mˆi, and hits his second shot 189.0 m with a displacement Δ→r2=172.0mˆi+80.3mˆj. What is the final displacement of the golf ball from where it started?

a) Option a: Δ→r = (472.0ˆi + 80.3ˆj) m; Option b: Δ→r = (-472.0ˆi - 80.3ˆj) m
b) Option a: Δ→r = (128.0ˆi + 80.3ˆj) m; Option b: Δ→r = (-128.0ˆi - 80.3ˆj) m
c) Option a: Δ→r = (-128.0ˆi - 80.3ˆj) m; Option b: Δ→r = (472.0ˆi + 80.3ˆj) m
d) Option a: Δ→r = (-472.0ˆi - 80.3ˆj) m; Option b: Δ→r = (128.0ˆi + 80.3ˆj) m

Answer 1

The final displacement of the golf ball is found by adding the two displacement vectors. The result is a final displacement vector of Δ→r = (472.0 m→i + 80.3 m→j).

Step-by-step explanation:

The student has inquired about determining the final displacement of a golf ball from its starting point after two consecutive shots on a golf course. To find the final displacement vector, we add the two displacement vectors for the first and second shots. The first displacement vector is Δ→r1 = 300.0 mâ€i, and the second displacement vector is Δ→r2 = 172.0 mâ€i + 80.3 mâ€j. When we add these two vectors component-wise, we get:

Δ→r_final = Δ→r1 + Δ→r2

= (300.0 m + 172.0 m)→i + (0 m + 80.3 m)→j

= 472.0 m→i + 80.3 m→j

To find the final displacement of the golf ball, we need to add up the displacements of each shot. The first shot has a displacement of 300.0 mî and the second shot has a displacement of 172.0 mî + 80.3 mĵ. Adding these displacements together, we get a final displacement of 472.0 mî + 80.3 mĵ, which corresponds to Option a: Δ→r = (472.0î + 80.3ĵ) m.

Therefore, the final displacement of the golf ball from where it started is Δ→r = (472.0 m→i + 80.3 m→j), which corresponds to option (a) in the question.