Question

for problems 32 - 35, refer to figure 24.

1. the diagram at the right shows the path of a ship that sails at a constant velocity of 42 km/h east. what is the ships position when it reaches point c, relative to the starting point, a, if it sails from point b to point c in exactly 1.5 h?
2. another ship starts at the same time from point b, but its average velocity is 58 km/h east. what is its position, relative to a, after 1.5 h?
3. what would a ships position be if that ship started at point b and traveled at an average velocity of 35 km/h west to point d in a time period of 1.2 h?
4. challenge suppose two ships start from point b and travel west. one ship travels at an average velocity of 35 km/h for 2.2 h. another ship travels at an average velocity of 26 km/h for 2.5 h. what is the final position of each ship?

Explanation:

for 32:

Step1: Calculate BC distance

$BC = 42 \, \text{km/h} \times 1.5 \, \text{h} = 63 \, \text{km}$

Step2: Position relative to A

$25 \, \text{km} + 63 \, \text{km} = 88 \, \text{km}$

for 33:

Step1: Calculate distance from B

$58 \, \text{km/h} \times 1.5 \, \text{h} = 87 \, \text{km}$

Step2: Position relative to A

$25 \, \text{km} + 87 \, \text{km} = 112 \, \text{km}$

for 34:

Step1: Calculate west distance from B

$35 \, \text{km/h} \times 1.2 \, \text{h} = 42 \, \text{km}$

Step2: Position relative to A

$25 \, \text{km} - 42 \, \text{km} = -17 \, \text{km}$

for 35:

Step1: First ship west distance

$35 \, \text{km/h} \times 2.2 \, \text{h} = 77 \, \text{km}$

Step2: First ship position relative to A

$25 \, \text{km} - 77 \, \text{km} = -52 \, \text{km}$

Step3: Second ship west distance

$26 \, \text{km/h} \times 2.5 \, \text{h} = 65 \, \text{km}$

Step4: Second ship position relative to A

$25 \, \text{km} - 65 \, \text{km} = -40 \, \text{km}$

Answer:

1. 88 km east of A
2. 112 km east of A
3. -17 km (17 km west of A)
4. First ship: -52 km (52 km west of A), Second ship: -40 km (40 km west of A)