A US Coast Guard cutter is chasing a ship suspected of running contraband cigars out of Cuba. The cutter's trip can be divided into three legs: it travels with a constant velocity of 40.1 km/hr for 1 hour and 45.0 minutes at a navigational direction of 260°; then it goes 41.3 km/hr for 51.0 minutes with a navigational direction of 275° and finally, it goes 58.4 km/hr for 33.0 minutes with a navigational direction of 329°. Provide answers in units of km and hours, and assume the cutter started at the origin.
HINT: Recall that you must have unit consistency. Convert the velocity and time data into displacements, and then add the vectors.
A. What is the cutter's final displacement? @ °
B. What is the cutter's average velocity? @ °
C. What is the cutter's average speed?
A. 120km/h, 67 degrees E of S
B. 38.1 km/h, 67 degrees E of S
C. 44.3 km/h
To solve this problem, we need to break down the cutter's trip into three legs and find the displacement for each leg. Then we can add these displacements to find the final displacement. We can also find the average velocity and average speed by using the total displacement and total time.
Let's start with the first leg:
Leg 1:
Velocity: 40.1 km/hr
Time: 1 hour and 45.0 minutes = 1.75 hours
Direction: 260°
To find the displacement for this leg, we can use the formula:
Displacement = Velocity * Time
Displacement for Leg 1 = 40.1 km/hr * 1.75 hours
Next, let's move on to the second leg:
Leg 2:
Velocity: 41.3 km/hr
Time: 51.0 minutes = 0.85 hours
Direction: 275°
Displacement for Leg 2 = 41.3 km/hr * 0.85 hours
Finally, let's calculate the third leg:
Leg 3:
Velocity: 58.4 km/hr
Time: 33.0 minutes = 0.55 hours
Direction: 329°
Displacement for Leg 3 = 58.4 km/hr * 0.55 hours
Now that we have the displacements for each leg, we can find the total displacement by adding them:
Total Displacement = Displacement Leg 1 + Displacement Leg 2 + Displacement Leg 3
Next, we can calculate the average velocity and average speed. The average velocity is the total displacement divided by the total time taken. The average speed is the total distance traveled divided by the total time taken.
Average Velocity = Total Displacement / Total Time
Average Speed = Total Distance / Total Time
Finally, we can convert the total displacement, average velocity, and average speed into the requested units of km and hours.
A. To find the cutter's final displacement, add the three displacements calculated above. The result will be in km.
B. To find the cutter's average velocity, divide the total displacement by the total time and find the direction using vector addition.
C. To find the cutter's average speed, divide the total distance traveled by the total time.
Please note that the calculations for the displacements, total displacement, average velocity, and average speed are not provided in the question and will need to be done separately using the given values.