Question

A scuba diver makes a slow descent into the depths of the ocean. His vertical position with respect to a boat on the surface changes several times. He makes the first stop 9.0 m from the boat but has a problem with equalizing the pressure, so he ascends 3.0 m and then continues descending for another 12.0 m to the second stop. From there, he ascends 4 m and then descends for 18.0 m, ascends again for 7 m and descends again for 24.0 m, where he makes a stop, waiting for his buddy. Assuming the positive direction up to the surface, express his net vertical displacement vector in terms of the unit vector. What is his distance to the boat?

a) ( hat{i} + 3hat{j} ); 30.0 m
b) ( -hat{i} - 6hat{j} ); 36.0 m
c) ( 2hat{i} + 8hat{j} ); 21.0 m
d) ( -4hat{i} - 6hat{j} ); 42.0 m

Answer 1

The net vertical displacement of the scuba diver, assuming the positive direction is up to the surface, is -49κj, and the distance to the boat is 49 m. The correct answer is not listed in the student's provided options, but the closest is option D.

Step-by-step explanation:

The student's question is related to net vertical displacement and distance measurement in a physics context involving vectors and displacement. To solve for the scuba diver's net vertical displacement, we need to add up his vertical movements, taking into account whether they are ascents (positive) or descents (negative).

First stop descent: -9.0 m

Ascent due to pressure issue: +3.0 m

Second stop descent: -12.0 m

Ascent: +4.0 m

Third stop descent: -18.0 m

Ascent: +7.0 m

Final stop descent: -24.0 m

Net vertical displacement: -9 + 3 - 12 + 4 - 18 + 7 - 24 = -49 m

Expressed in terms of the unit vector, the net vertical displacement vector would be -49κj. To find the distance to the boat, we take the absolute value of the net displacement because the distance is a scalar and is always positive: distance = |net displacement| = 49 m.

The correct answer to the student's question is: ( -hat{i} - 6hat{j} ); 49.0 m, which is not listed in the provided options.