A cruise ship travels at 22 knots. [1 knot is 1.852 kilometres per hour.] Convert this speed into metres per second.
The Correct Answer and Explanation is:
To convert the speed of the cruise ship from knots to metres per second, we need to follow these steps:
Step 1: Convert knots to kilometres per hour
The problem states that the cruise ship travels at 22 knots, and 1 knot is equal to 1.852 kilometres per hour. To find the speed in kilometres per hour, we multiply the number of knots by the conversion factor:Speed in km/h=22 knots×1.852 kmh=40.744 km/h\text{Speed in km/h} = 22 \, \text{knots} \times 1.852 \, \frac{\text{km}}{\text{h}} = 40.744 \, \text{km/h}Speed in km/h=22knots×1.852hkm=40.744km/h
Step 2: Convert kilometres per hour to metres per second
Next, we convert kilometres per hour (km/h) into metres per second (m/s). To do this, we use the fact that:1 km=1000 mand1 hour=3600 seconds1 \, \text{km} = 1000 \, \text{m} \quad \text{and} \quad 1 \, \text{hour} = 3600 \, \text{seconds}1km=1000mand1hour=3600seconds
Thus, to convert from kilometres per hour to metres per second, we divide the speed in km/h by 3.6:Speed in m/s=40.744 km/h3.6=11.33 m/s\text{Speed in m/s} = \frac{40.744 \, \text{km/h}}{3.6} = 11.33 \, \text{m/s}Speed in m/s=3.640.744km/h=11.33m/s
Final Answer:
The speed of the cruise ship is approximately 11.33 metres per second.
Explanation:
We began by converting knots to kilometres per hour by using the conversion factor of 1 knot = 1.852 km/h. Then, we converted the speed in km/h to m/s by dividing by 3.6, since 1 kilometre is 1000 metres and 1 hour is 3600 seconds. This gives us the cruise ship’s speed in metres per second, which is a more commonly used unit for velocity in physics and engineering contexts.
