A car travels along a straight road, heading east for one hour then traveling for thirty minutes on another road that leads northeast. If the car has maintained a constant speed of forty miles an hour, how far is it from its starting position
X = hor = 40 mi/h * 1 h + 40 mi/h * 0.5 h * cos45 = 40 + 14.1 = 54.1 mi.
Y = ver = 40 mi/h * 0.5 h * sin45 = 14.1 mi.
tanA = Y/X = 14.1 / 54.1 = 0.2606,
A = 14.6 deg.
d = x / cosA = 54,1 / cos14.6= 55.9 mi.
from starting position.
8
To find the distance from the car's starting position, we need to calculate the distance it covered while moving east and northeast.
First, let's find the distance covered while moving east. The car travels at a constant speed of 40 miles per hour for one hour. Therefore, the distance covered while moving east is:
Distance = Speed × Time
Distance = 40 miles/hour × 1 hour
Distance = 40 miles
Now, let's find the distance covered while moving northeast. The car travels at a constant speed of 40 miles per hour for 30 minutes, which is equivalent to 0.5 hours. The direction northeast forms a right triangle, so we can use the Pythagorean theorem to find the distance. In this case, the adjacent and opposite sides of the triangle are the same length.
Distance = √(adjacent^2 + opposite^2)
Distance = √(40 miles/hour × 0.5 hours)^2 + (40 miles/hour × 0.5 hours)^2
Distance = √(20 miles)^2 + (20 miles)^2
Distance = √(400 miles^2 + 400 miles^2)
Distance = √(800 miles^2)
Distance = 28.28 miles (approx.)
To find the total distance from the car's starting position, we can add the distance covered while moving east to the distance covered while moving northeast:
Total distance = Distance (east) + Distance (northeast)
Total distance = 40 miles + 28.28 miles
Total distance = 68.28 miles (approx.)
Therefore, the car is approximately 68.28 miles away from its starting position.