Instructions
Complete the following problems and show your work where required. Use the space provided to write your answers.
1. An airplane is preparing for takeoff. If its initial velocity is 50 m/s and it accelerates uniformly at 2 m/s² for 10 seconds, what is its takeoff distance? Use the formula: distance = (final velocity² - initial velocity²) / (2 * acceleration).
2. A small plane consumes fuel at a rate of 20 liters per hour. If it flies 300 km to its destination and returns, but uses an additional 10% fuel on the return trip due to headwinds, how many liters of fuel are needed for the round trip?
3. The cruising altitude of a plane is 35,000 feet. If the air pressure at this altitude is 1/5th of the pressure at sea level, and the pressure at sea level is 14.7 psi, what is the pressure at 35,000 feet? Use the formula: P = P0 * e^(-h/H), where h is the altitude gain and H is the scale height (approximately 7,000 meters).
4. A plane flies a heading of 45 degrees for 200 miles, then turns 90 degrees to the north and flies another 150 miles. What is its resultant displacement vector from the starting point? Use vector addition and show your work.
5. If a jetliner lands with an initial speed of 150 knots and comes to a stop over a runway of 3,000 meters, what is the average deceleration? Use the formula: v² = u² + 2 * a * s, where v is the final velocity (0), u is the initial velocity, a is the acceleration, and s is the distance.
6. An airplane has fixed costs of $50,000 and variable costs of $100 per passenger. If tickets are sold at $150 each, how many passengers must be sold to break even? Use the formula: Fixed Costs + (Variable Costs * Passengers) = (Ticket Price * Passengers).
7. A plane is flying at an angle of 30 degrees above the horizontal. Its engines produce 2,000 N of thrust each. What is the total vertical component of the thrust? Use the formula: F = T * sin(theta).
8. Air traffic control informs a pilot that an aircraft is 15 km away and closing in at a relative speed of 150 m/s. How many seconds until the planes are at the same point? Use the formula: time = distance / speed.
9. A jet engine consumes fuel at a rate of 500 kg per hour. If the plane flies for 5 hours, but also carries an additional 1,000 kg of reserve fuel, what is the total fuel consumption? Use the formula: Total Fuel = (Fuel Rate * Time) + Reserve Fuel.
10. The ground crew needs to unload 500 bags from a plane in 10 minutes. If they can unload 3 bags per person per minute, how many crew members are needed to meet the deadline? Use the formula: Number of Crew = (Total Bags / Time) / Rate per Person.