
The mass of the parasitic wasp Caraphractus cintus can be as small as 5 x 10-6 kg. What is this mass in (a) grams, and (b) milligrams? [a. 0.005g, b. 5mg]




Vesna Vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles, 551 yards. What is this distance in meters? [10,159m]




How many seconds are there in (a) one hour and thirty-five minutes, and (b) one day? [a. 5700s, b. 86,400s]







Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)? [a. 54.71km/h, b. 15.20m/s]


























Let's break down each question with detailed solutions:

### 1. **Mass of the parasitic wasp Caraphractus cintus**
The mass is given as \(5 \times 10^{-6} \, \text{kg}\).

- **(a) Convert to grams:**

  Since \(1 \, \text{kg} = 1000 \, \text{g}\), we can convert the mass from kilograms to grams:
  \[
  5 \times 10^{-6} \, \text{kg} \times 1000 \, \text{g/kg} = 0.005 \, \text{g}
  \]

- **(b) Convert to milligrams:**

  Since \(1 \, \text{g} = 1000 \, \text{mg}\), we can convert from grams to milligrams:
  \[
  0.005 \, \text{g} \times 1000 \, \text{mg/g} = 5 \, \text{mg}
  \]

### 2. **Vesna Vulovic's fall**
The distance she fell is \(6 \, \text{miles} + 551 \, \text{yards}\).

- **Convert miles to meters:**

  Since \(1 \, \text{mile} = 1609.34 \, \text{meters}\),
  \[
  6 \, \text{miles} \times 1609.34 \, \text{m/mile} = 9656.04 \, \text{meters}
  \]

- **Convert yards to meters:**

  Since \(1 \, \text{yard} = 0.9144 \, \text{meters}\),
  \[
  551 \, \text{yards} \times 0.9144 \, \text{meters/yard} = 503.46 \, \text{meters}
  \]

- **Total distance in meters:**
  \[
  9656.04 \, \text{meters} + 503.46 \, \text{meters} = 10,159.5 \, \text{meters}
  \]

  Rounding to the nearest meter: \(10,159 \, \text{meters}\).

### 3. **Time conversions**
- **(a) One hour and thirty-five minutes in seconds:**

  Since \(1 \, \text{hour} = 3600 \, \text{seconds}\) and \(1 \, \text{minute} = 60 \, \text{seconds}\):
  \[
  1 \, \text{hour} \times 3600 \, \text{s/hour} = 3600 \, \text{s}
  \]
  \[
  35 \, \text{minutes} \times 60 \, \text{s/minute} = 2100 \, \text{s}
  \]
  \[
  \text{Total time} = 3600 \, \text{s} + 2100 \, \text{s} = 5700 \, \text{s}
  \]

- **(b) One day in seconds:**

  Since \(1 \, \text{day} = 24 \, \text{hours}\) and \(1 \, \text{hour} = 3600 \, \text{seconds}\):
  \[
  24 \, \text{hours} \times 3600 \, \text{s/hour} = 86,400 \, \text{s}
  \]

### 4. **Bicyclist's speed in the Tour de France**
The speed is given as \(34.0 \, \text{mi/h}\).

- **(a) Convert to kilometers per hour (km/h):**

  Since \(1 \, \text{mile} = 1.60934 \, \text{kilometers}\),
  \[
  34.0 \, \text{mi/h} \times 1.60934 \, \text{km/mile} = 54.71756 \, \text{km/h}
  \]

  Rounding to two decimal places: \(54.71 \, \text{km/h}\).

- **(b) Convert to meters per second (m/s):**

  Since \(1 \, \text{km/h} = \frac{1000 \, \text{m}}{3600 \, \text{s}} \approx 0.27778 \, \text{m/s}\):
  \[
  54.71756 \, \text{km/h} \times 0.27778 \, \text{m/s per km/h} = 15.199 \, \text{m/s}
  \]

  Rounding to two decimal places: \(15.20 \, \text{m/s}\).

---

Do you want more details or have any questions about any of these conversions?

### 5 Related Questions:
1. What is the mass of the wasp in micrograms?
2. How many feet did Vesna Vulovic fall?
3. How many seconds are in two hours?
4. What would be the speed of the bicyclists in feet per second?
5. How would you convert 100 kilometers per hour to meters per second?

### Tip:
Always double-check unit conversions by confirming basic equivalences (e.g., 1 km = 1000 m, 1 hour = 3600 seconds).

The mass of the parasitic wasp Caraphractus cintus can be as small as 5 x 10^-6 kg. What is this mass in (a) grams, and (b) milligrams?
Vesna Vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles, 551 yards. What is this distance in meters?
How many seconds are there in (a) one hour and thirty-five minutes, and (b) one day?
Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)?

Solve real-world problems involving unit conversions. Find the mass of the parasitic wasp Caraphractus cintus in grams and milligrams, calculate Vesna Vulovic's fall in meters, convert time to seconds, and find the speed of Tour de France cyclists in kilometers per hour and meters per second. Ideal for students in Grades 6-8.

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