(d) The South African born entrepreneur, Elon Musk, is planning to launch a spacecraft that will land on Mars sometime in the future. His company, SpaceX, wants to build a permanent human settlement on Mars. The first human colony on the red planet will live inside domes. Assuming that Mars is about 266666667 km from Earth, how long would it take, in days, for a spacecraft to reach Mars travelling at a speed of \( 28500 \mathrm{~km} / \mathrm{h} \) ? (e) Leanne drives 282 km from East London to Port Elizabeth travelling at an average speed of \( 94 \mathrm{~km} / \mathrm{h} \). She leaves East London at 07:00. At what time will she arrive in Port Elizabeth? (f) (1) A car travels at an average speed of \( 100 \mathrm{~km} / \mathrm{h} \) for 4 hours 15 minutes. At what speed must the car travel to cover the same distance in 5 hours 30 minutes? (2) An object travelling at a constant speed moves 80 metres in 72 minutes. How far, travelling at the same speed, will the object move in 3 hours? (3) An athlete runs 4 km in 24 minutes. How long will it take the athlete to rur 15 km at the same constant speed? (4) A car travels 165 km at an average speed of \( 100 \mathrm{~km} / \mathrm{h} \). How far will the

Certainly! Let's address each of your questions step by step. --- ### **(d) Time for a Spacecraft to Reach Mars** **Given:** - **Distance to Mars:** 266,666,667 km - **Speed of Spacecraft:** 28,500 km/h **Calculation:** 1. **Time (in hours) = Distance / Speed** \[ \text{Time} = \frac{266,666,667 \text{ km}}{28,500 \text{ km/h}} \approx 9,368.63 \text{ hours} \] 2. **Convert Hours to Days:** \[ \text{Time in days} = \frac{9,368.63 \text{ hours}}{24 \text{ hours/day}} \approx 390.36 \text{ days} \] **Answer:** It would take approximately **390 days** for the spacecraft to reach Mars at a speed of 28,500 km/h. --- ### **(e) Arrival Time in Port Elizabeth** **Given:** - **Distance:** 282 km - **Average Speed:** 94 km/h - **Departure Time:** 07:00 **Calculation:** 1. **Time = Distance / Speed** \[ \text{Time} = \frac{282 \text{ km}}{94 \text{ km/h}} = 3 \text{ hours} \] 2. **Determine Arrival Time:** \[ \text{Departure Time} + \text{Travel Time} = 07:00 + 3 \text{ hours} = 10:00 \] **Answer:** Leanne will arrive in Port Elizabeth at **10:00 AM**. --- ### **(f) Various Motion Problems** #### **(1) Adjusting Speed for the Same Distance** **Given:** - **Initial Speed:** 100 km/h - **Initial Time:** 4 hours 15 minutes (4.25 hours) - **Desired Time:** 5 hours 30 minutes (5.5 hours) **Calculation:** 1. **Distance Covered Initially:** \[ \text{Distance} = \text{Speed} \times \text{Time} = 100 \text{ km/h} \times 4.25 \text{ h} = 425 \text{ km} \] 2. **Required Speed for Same Distance in Desired Time:** \[ \text{Required Speed} = \frac{\text{Distance}}{\text{Desired Time}} = \frac{425 \text{ km}}{5.5 \text{ h}} \approx 77.27 \text{ km/h} \] **Answer:** The car must travel at approximately **77.3 km/h** to cover the same distance in 5 hours and 30 minutes. --- #### **(2) Distance Covered in 3 Hours** **Given:** - **Distance in 72 minutes:** 80 meters - **Desired Time:** 3 hours (180 minutes) **Calculation:** 1. **Determine Speed:** \[ \text{Speed} = \frac{80 \text{ meters}}{72 \text{ minutes}} \approx 1.111 \text{ m/min} \] 2. **Distance in 180 Minutes:** \[ \text{Distance} = \text{Speed} \times \text{Time} = 1.111 \text{ m/min} \times 180 \text{ min} = 200 \text{ meters} \] **Answer:** The object will move **200 meters** in 3 hours at the same speed. --- #### **(3) Time to Run 15 km** **Given:** - **Distance:** 4 km - **Time:** 24 minutes - **Desired Distance:** 15 km **Calculation:** 1. **Determine Speed:** \[ \text{Speed} = \frac{4 \text{ km}}{24 \text{ minutes}} = \frac{1}{6} \text{ km/min} \] 2. **Time to Run 15 km:** \[ \text{Time} = \frac{15 \text{ km}}{\frac{1}{6} \text{ km/min}} = 15 \times 6 = 90 \text{ minutes} = 1 \text{ hour and } 30 \text{ minutes} \] **Answer:** It will take the athlete **1 hour and 30 minutes** to run 15 km at the same constant speed. --- #### **(4) Incomplete Question** **Given:** - **Distance Traveled:** 165 km - **Average Speed:** 100 km/h - **Question:** "How far will the..." It appears that part (4) of your question is incomplete. Could you please provide the rest of the question so I can assist you accurately? --- If you have any further questions or need clarification on any of the parts, feel free to ask!