A jet pilot flies 100 km north to an airport, then 1400 km east to another airport, then finally 1000 km north to a third airport.
a) What is the total distance covered by the plane?
b) How far is the pilot from the original point of take
(a) 100+1400+1000 = 2500 km
(b) Since he ends up 1100 N and 1400E,
d^2 = 1100^2 + 1400^2
a) To find the total distance covered by the plane, we need to calculate the sum of the distances traveled in each direction. The plane traveled 100 km north, 1400 km east, and finally 1000 km north. Therefore, the total distance covered by the plane is 100 + 1400 + 1000 = 2500 km.
b) To find how far the pilot is from the original point of takeoff, we can use the Pythagorean theorem. The pilot traveled 100 km north and then 1000 km north, resulting in a total northward distance of 100 + 1000 = 1100 km. The plane traveled 1400 km east, so we have a right triangle with one leg 1100 km and the other leg 1400 km.
Using the Pythagorean theorem, we can calculate the distance from the original point of takeoff:
Distance = √(1100^2 + 1400^2) = √(1210000 + 1960000) = √3170000 ≈ 1781.86 km
Therefore, the pilot is approximately 1781.86 km from the original point of takeoff.
To find the total distance covered by the plane, we need to calculate the sum of the distances traveled in each direction.
a) Let's calculate the distance covered in each direction:
- Distance traveled north: 100 km
- Distance traveled east: 1400 km
- Distance traveled north again: 1000 km
To find the total distance covered by the plane, we add these distances together:
Total distance = 100 km + 1400 km + 1000 km = 2500 km
Therefore, the total distance covered by the plane is 2500 km.
b) To find how far the pilot is from the original point of takeoff, we need to calculate the straight-line distance between the starting point and the final destination.
Since the pilot flew 100 km north, 1400 km east, and then 1000 km north, we can imagine this as a right-angled triangle, with the legs representing the distances traveled in the north and east directions, and the hypotenuse representing the straight-line distance.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse (c) as follows:
c^2 = a^2 + b^2
Where a and b are the distances traveled in each direction.
Applying this formula, we have:
c^2 = (100 km)^2 + (1400 km)^2
Calculating:
c^2 = 10000 km^2 + 1960000 km^2
c^2 = 1970000 km^2
Taking the square root of both sides, we find:
c = √(1970000 km^2)
c ≈ 1403.56 km
Therefore, the pilot is approximately 1403.56 km from the original point of takeoff.