EXERCISE 39 1. Convert each of the following rates to metres per second: a) \( 40 \mathrm{~km} / \mathrm{h} \) b) \( 120 \mathrm{~km} / \mathrm{h} \) C) \( 5 \mathrm{~km} / \mathrm{h} \) d) \( 12 \mathrm{~km} / \mathrm{h} \) 2. Convert each of the following rates to kilometres per hour a) \( 4 \mathrm{~m} / \mathrm{s} \) b) \( 15 \mathrm{~m} / \mathrm{s} \) c) \( 30 \mathrm{~m} / \mathrm{s} \) d) \( 3600 \mathrm{~m} / \mathrm{s} \) 3. If a washing machine spins at 1200 revolutions per minute, how many revolutions will it complete in one second? 4. The speedometer of a sports car shows that the car's top speed is \( 370 \mathrm{~km} / \mathrm{h} \). What is this speed in \( \mathrm{m} / \mathrm{s} \) ? 5. The top speed of a 747 Jumbo Jet is \( 245 \mathrm{~m} / \mathrm{s} \). Convert this speed to \( \mathrm{km} / \mathrm{h} \). 6. The Argus Cycle Tour is a circular cycle race starting in the Cape Town city centre, going around the Cape Peninsula and back to the city, ending at Cape Town Stadium. This race can vary from 104 km to 110 km in length, depending on the necessary detours at the time of the race. In 2008 , the length of the race was 109 km , and Robble Hunter completed the race in a record time of \( 2: 27: 29 \). In 2007, Anke Eriank-Moore set a ladies record of \( 2: 48: 29 \), also over a distance of 109 km . The oldest person to complete the race is Japie Malan, who was 90 years old when he completed the race in a time of 6:48:52 in 2010. a) What was Robbie's average speed for this race in \( \mathrm{km} / \mathrm{min} \) ? b) Convert the average speed obtained in a) to \( \mathrm{km} / \mathrm{h} \). c) Convert the ladies record to a rate of \( \mathrm{km} / \mathrm{min} \). d) What was the average speed of the oldest person to complete the Argus Cycle Tour in 2010? Give your answer in \( \mathrm{km} / \mathrm{h} \). 7. Sizwe drives from Durban to Polokwane - a distance of 745 km . If the journey takes him 7 hours and 20 minutes, what is his average speed in \( \mathrm{km} / \mathrm{h} \) ?

Sure! Let's work through each of the exercises step by step. --- ### **Exercise 39** #### **1. Convert each of the following rates to metres per second (m/s):** The conversion factor between kilometers per hour (km/h) and meters per second (m/s) is: \[ 1\, \text{km/h} = \frac{1000\, \text{meters}}{3600\, \text{seconds}} = \frac{5}{18}\, \text{m/s} \] **a) \( 40\, \text{km/h} \)** \[ 40\, \text{km/h} \times \frac{5}{18}\, \frac{\text{m}}{\text{s}} = \frac{200}{18}\, \text{m/s} \approx 11.11\, \text{m/s} \] **b) \( 120\, \text{km/h} \)** \[ 120\, \text{km/h} \times \frac{5}{18}\, \frac{\text{m}}{\text{s}} = \frac{600}{18}\, \text{m/s} = 33.33\, \text{m/s} \] **c) \( 5\, \text{km/h} \)** \[ 5\, \text{km/h} \times \frac{5}{18}\, \frac{\text{m}}{\text{s}} = \frac{25}{18}\, \text{m/s} \approx 1.39\, \text{m/s} \] **d) \( 12\, \text{km/h} \)** \[ 12\, \text{km/h} \times \frac{5}{18}\, \frac{\text{m}}{\text{s}} = \frac{60}{18}\, \text{m/s} \approx 3.33\, \text{m/s} \] --- #### **2. Convert each of the following rates to kilometres per hour (km/h):** The conversion factor between meters per second (m/s) and kilometers per hour (km/h) is: \[ 1\, \text{m/s} = \frac{3600\, \text{seconds}}{1000\, \text{meters}} = \frac{18}{5}\, \text{km/h} \] **a) \( 4\, \text{m/s} \)** \[ 4\, \text{m/s} \times \frac{18}{5}\, \frac{\text{km}}{\text{h}} = \frac{72}{5}\, \text{km/h} = 14.4\, \text{km/h} \] **b) \( 15\, \text{m/s} \)** \[ 15\, \text{m/s} \times \frac{18}{5}\, \frac{\text{km}}{\text{h}} = \frac{270}{5}\, \text{km/h} = 54\, \text{km/h} \] **c) \( 30\, \text{m/s} \)** \[ 30\, \text{m/s} \times \frac{18}{5}\, \frac{\text{km}}{\text{h}} = \frac{540}{5}\, \text{km/h} = 108\, \text{km/h} \] **d) \( 3600\, \text{m/s} \)** \[ 3600\, \text{m/s} \times \frac{18}{5}\, \frac{\text{km}}{\text{h}} = \frac{64800}{5}\, \text{km/h} = 12960\, \text{km/h} \] --- #### **3. Revolutions per Minute to Revolutions per Second** **Given:** A washing machine spins at 1200 revolutions per minute (rpm). To convert to revolutions per second (rps): \[ \text{Revolutions per second} = \frac{\text{Revolutions per minute}}{60} \] \[ \text{Revolutions per second} = \frac{1200}{60} = 20\, \text{rps} \] --- #### **4. Convert the car's top speed from km/h to m/s** **Given:** Top speed = \( 370\, \text{km/h} \) Using the conversion factor \( 1\, \text{km/h} = \frac{5}{18}\, \text{m/s} \): \[ 370\, \text{km/h} \times \frac{5}{18}\, \frac{\text{m}}{\text{s}} = \frac{1850}{18}\, \text{m/s} \approx 102.78\, \text{m/s} \] --- #### **5. Convert the Jumbo Jet's speed from m/s to km/h** **Given:** Top speed = \( 245\, \text{m/s} \) Using the conversion factor \( 1\, \text{m/s} = \frac{18}{5}\, \text{km/h} \): \[ 245\, \text{m/s} \times \frac{18}{5}\, \frac{\text{km}}{\text{h}} = \frac{4410}{5}\, \text{km/h} = 882\, \text{km/h} \] --- #### **6. Argus Cycle Tour Speed Calculations** **Given:** - Distance = 109 km - Robbie Hunter's time = 2 hours, 27 minutes, 29 seconds (\( 2:27:29 \)) - Anke Eriank-Moore's time (ladies record) = 2 hours, 48 minutes, 29 seconds (\( 2:48:29 \)) - Japie Malan's time = 6 hours, 48 minutes, 52 seconds (\( 6:48:52 \)) **a) Robbie's average speed in km/min** First, convert Robbie's time to minutes. \[ 2\, \text{hours} = 2 \times 60 = 120\, \text{minutes} \] \[ 27\, \text{minutes} = 27\, \text{minutes} \] \[ 29\, \text{seconds} = \frac{29}{60}\, \text{minutes} \approx 0.483\, \text{minutes} \] \[ \text{Total time} = 120 + 27 + 0.483 = 147.483\, \text{minutes} \] \[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{109\, \text{km}}{147.483\, \text{min}} \approx 0.740\, \text{km/min} \] **b) Convert the average speed obtained in a) to km/h** \[ 0.740\, \text{km/min} \times 60\, \frac{\text{min}}{\text{h}} = 44.4\, \text{km/h} \] **c) Convert the ladies record to a rate of km/min** First, convert Anke's time to minutes. \[ 2\, \text{hours} = 2 \times 60 = 120\, \text{minutes} \] \[ 48\, \text{minutes} = 48\, \text{minutes} \] \[ 29\, \text{seconds} = \frac{29}{60}\, \text{minutes} \approx 0.483\, \text{minutes} \] \[ \text{Total time} = 120 + 48 + 0.483 = 168.483\, \text{minutes} \] \[ \text{Average speed} = \frac{109\, \text{km}}{168.483\, \text{min}} \approx 0.648\, \text{km/min} \] **d) Average speed of the oldest person in km/h** **Given:** Japie Malan's time = 6 hours, 48 minutes, 52 seconds. First, convert time to hours. \[ 6\, \text{hours} = 6\, \text{hours} \] \[ 48\, \text{minutes} = \frac{48}{60} = 0.8\, \text{hours} \] \[ 52\, \text{seconds} = \frac{52}{3600} \approx 0.0144\, \text{hours} \] \[ \text{Total time} = 6 + 0.8 + 0.0144 = 6.8144\, \text{hours} \] \[ \text{Average speed} = \frac{109\, \text{km}}{6.8144\, \text{h}} \approx 16\, \text{km/h} \] *Note:* The exact value is approximately 16 km/h. --- #### **7. Sizwe's Average Speed** **Given:** - Distance = 745 km - Time = 7 hours and 20 minutes First, convert time to hours. \[ 20\, \text{minutes} = \frac{20}{60} = 0.333\, \text{hours} \] \[ \text{Total time} = 7 + 0.333 = 7.333\, \text{hours} \] \[ \text{Average speed} = \frac{745\, \text{km}}{7.333\, \text{h}} \approx 101.5\, \text{km/h} \] --- ### **Summary of Answers** 1. **Rates converted to m/s:** - a) 40 km/h ≈ 11.11 m/s - b) 120 km/h = 33.33 m/s - c) 5 km/h ≈ 1.39 m/s - d) 12 km/h ≈ 3.33 m/s 2. **Rates converted to km/h:** - a) 4 m/s = 14.4 km/h - b) 15 m/s = 54 km/h - c) 30 m/s = 108 km/h - d) 3600 m/s = 12960 km/h 3. **Revolutions:** - 1200 rpm = 20 rps 4. **Car's top speed:** - 370 km/h ≈ 102.78 m/s 5. **Jumbo Jet's speed:** - 245 m/s = 882 km/h 6. **Argus Cycle Tour:** - a) Robbie's average speed ≈ 0.740 km/min - b) ≈ 44.4 km/h - c) Ladies record ≈ 0.648 km/min - d) Oldest person's average speed ≈ 16 km/h 7. **Sizwe's average speed:** - ≈ 101.5 km/h --- If you have any further questions or need clarifications on any of these solutions, feel free to ask!