An airplane flies due north from a starting point at 234.6 mph for 40 minutes. Then turns flying 20 minutes at 252 mph in the direction N 20 degree 31 minutes East. How many miles is the airplane from the starting point?
find the two distances:
northbound part = 234.6(40/60) = 156.4 miles
NE part = 252(20/60) = 84 miles
N 20°31' E = N 20.5166667 ° E
I see a triangle with sides 156.4 and 84 with an angle of 159.48333 between them.
by cosine law
x^2 = 156.4^2 + 84^2 - 2(156.4)(84)cos 159.48333
= ...
I will let you slug it out
(I got 236.9 miles)
To find the distance of the airplane from the starting point, we can break down the problem into two parts: the distance traveled due north and the distance traveled in the N20°31'E direction.
1. Distance traveled due north:
The airplane flies at a speed of 234.6 mph for 40 minutes. To convert the time to hours, we divide by 60: 40 minutes / 60 minutes per hour = 0.67 hours.
The formula to calculate distance is speed multiplied by time: distance = speed x time. Therefore, the distance traveled due north is 234.6 mph x 0.67 hours = 157.2 miles.
2. Distance traveled in the N20°31'E direction:
The airplane flies at a speed of 252 mph for 20 minutes. Converting 20 minutes to hours: 20 minutes / 60 minutes per hour = 0.33 hours.
To find the distance traveled in the N20°31'E direction, we first need to calculate the component of speed in the N20°31'E direction. To do this, we use trigonometry.
The component of speed in the N20°31'E direction is given by the equation: speed x cosine(angle). Plugging in the values: component of speed = 252 mph x cos(20°31').
The distance traveled in this direction is then the speed component multiplied by the time: distance = component of speed x time. Therefore, the distance traveled in the N20°31'E direction is (252 mph x cos(20°31')) x 0.33 hours.
To find the total distance from the starting point, we need to calculate the magnitude of the two distances traveled. This can be done using the Pythagorean theorem.
The total distance is given by: sqrt((distance due north)^2 + (distance in N20°31'E direction)^2).
Plugging in the values we calculated, the total distance from the starting point is sqrt(157.2^2 + [(252 mph x cos(20°31')) x 0.33 hours]^2). Calculate this expression to find the final answer.