A boat is moving eastward at 1.6 m/s parallel to a bank. Person A is standing on the bank and observes people B and C on the boat. (1) B is moving in the same direction as the boat at 2.1 m/s relative to the boat. What is the velocity of B as seen by A? (2) C is moving in the opposite direction as the boat at 2.7 m/s relative to the boat. What is the velocity of C as seen by A? (3) In 3.0 seconds, in which direction and by how many meters does C move relative to the bank?

1. Problem Description

A boat is moving eastward at 1.6 m/s parallel to a bank. Person A is standing on the bank and observes people B and C on the boat.

(1) B is moving in the same direction as the boat at 2.1 m/s relative to the boat. What is the velocity of B as seen by A?

(2) C is moving in the opposite direction as the boat at 2.7 m/s relative to the boat. What is the velocity of C as seen by A?

(3) In 3.0 seconds, in which direction and by how many meters does C move relative to the bank?

2. Solution Steps

(1) Since B is moving in the same direction as the boat, the velocities add up.

$v_{BA} = v_{boat, A} + v_{B, boat}$

$v_{BA} = 1.6 \text{ m/s} + 2.1 \text{ m/s} = 3.7 \text{ m/s}$ eastward.

(2) Since C is moving in the opposite direction as the boat, the velocities subtract.

$v_{CA} = v_{boat, A} - v_{C, boat}$

$v_{CA} = 1.6 \text{ m/s} - 2.7 \text{ m/s} = -1.1 \text{ m/s}$

The negative sign indicates westward direction. Therefore, C is moving westward at 1.1 m/s as seen by A.

(3) We already know the velocity of C relative to A, which is the bank. It is moving westward at 1.1 m/s.

The distance covered in 3.0 seconds is given by:

$d = v \times t$

$d = 1.1 \text{ m/s} \times 3.0 \text{ s} = 3.3 \text{ m}$

Therefore, C moves 3.3 m westward.

3. Final Answer

(1) Eastward at 3.7 m/s.

(2) Westward at 1.1 m/s.

(3) Westward 3.3 m.