Explanation:
Let's address each question step by step:
**3. Horse tied with a 2m long rope at a pole:**
a) **Distance around the pole:**
The horse takes one and a half rounds around the pole with the rope tightly stretched.
- The length of the rope is 2 meters.
- To calculate the distance around the pole for one round, we use the circumference formula of a circle:
\[
\text{Circumference} = 2 \pi \times \text{radius}
\]
Here, the radius \( r \) is the length of the rope, which is 2 meters. Therefore,
\[
\text{Circumference} = 2 \pi \times 2 = 4 \pi \text{ meters}
\]
- For one and a half rounds, the distance covered by the horse:
\[
\text{Distance} = 1.5 \times 4 \pi = 6 \pi \text{ meters}
\]
b) **Displacement of the horse:**
- Displacement is the straight-line distance from the starting point to the ending point.
Since the horse ends up where it started (after one and a half rounds), the displacement is equal to the radius of the circle formed by the rope, which is 2 meters.
**4. Odometer of an automobile:**
- An odometer measures the total distance traveled by the automobile.
**Comparison of speeds:**
- Convert the speed of the car from km/h to m/s:
\[
\text{Speed of car} = 36 \times \frac{1000}{3600} = 10 \text{ m/s}
\]
- Now, compare the speeds:
- Speed of scooter = 300 m/s
- Speed of car = 10 m/s
Clearly, the scooter is moving faster than the car because its speed is 300 m/s compared to the car's speed of 10 m/s.
**5. Average speed of the object:**
- The object travels 16 meters in 4 seconds and then another 16 meters in 2 seconds.
To find the average speed, use the formula:
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
- Total distance traveled = 16 meters + 16 meters = 32 meters
- Total time taken = 4 seconds + 2 seconds = 6 seconds
\[
\text{Average Speed} = \frac{32 \text{ meters}}{6 \text{ seconds}} = 5.33 \text{ m/s}
\]
Therefore, the average speed of the object is \( 5.33 \) meters per second.
