Question

A truck travels from point M northward for 30 min, then eastward

for one hour, then shifted N 30oW. if the constant speed is 85 kph,
how far directly from M, in km, will it be after 2 hours?
Explain.

Answer 1

To find the distance directly from point M after 2 hours, calculate the displacement in the northward and eastward directions and use the Pythagorean theorem to find the total distance.

Step-by-step explanation:

To find the distance directly from point M after 2 hours, we need to determine the displacement of the truck in the northward and eastward directions and then calculate the total distance using the Pythagorean theorem.

Distance traveled northward = speed * time = 85 km/h * 0.5 hours = 42.5 km

Distance traveled eastward = speed * time = 85 km/h * 1 hour = 85 km

The displacement in the northward direction is 42.5 km, and the displacement in the eastward direction is 85 km. Using the Pythagorean theorem, the distance directly from point M after 2 hours is:

Distance = sqrt(displacement north^2 + displacement east^2) = sqrt((42.5 km)^2 + (85 km)^2) = sqrt(1806.25 + 7225) = sqrt(9031.25) = 95.1 km

Therefore, the truck will be approximately 95.1 km directly from point M after 2 hours.

Answer 2

The direct distance from Point M after 2 hours can be calculated using trigonometry and vector components based on the truck's northward, eastward, and N 30°W travels at a speed of 85 kph, and applying the Pythagorean theorem.

Step-by-step explanation:

The question involves calculating the shortest direct distance from the starting point, Point M, after the truck has traveled in three different directions at a constant speed of 85 kph. To solve this, we'll need to use the concepts of vectors and trigonometry.

First Leg: The truck travels northward for 30 minutes, which is 0.5 hours. At 85 kph, the distance covered in this leg is 0.5 hours × 85 kph = 42.5 km north.

Second Leg: Next, the truck travels eastward for one hour. Distance covered = 1 hour × 85 kph = 85 km east.

Third Leg: The truck then shifts to N 30°W and continues for another 0.5 hours (since the total travel time is 2 hours). To find the distance in this leg, we must first find the northward and westward components using sine and cosine:

• Northward: 85 kph × cos(30°) × 0.5 hours
• Westward: 85 kph × sin(30°) × 0.5 hours

Finally, we calculate the total northward and eastward components and use the Pythagorean theorem to find the direct distance from Point M:

• Total northward: 42.5 km + (85 × cos(30°) × 0.5)
• Total eastward: 85 km - (85 × sin(30°) × 0.5)

Apply Pythagorean theorem: √(Total northward² + Total eastward²)

The calculated value will be the direct distance from Point M after 2 hours.