a plane is headed north with a velocity of 400km/hr and west wind blowing at 70km/hr.find the distance of the plane from its base in 2hrs
A student in Lakehead university
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To find the distance of the plane from its base in 2 hours, we can use the Pythagorean theorem since the plane is moving both north and west.
Step 1: Find the horizontal distance covered by the plane.
Since the plane is moving north and the wind is blowing west, the horizontal component of the velocity of the plane is 400 km/hr - 70 km/hr = 330 km/hr (opposite direction to the wind).
Using the formula distance = speed × time, the horizontal distance covered by the plane in 2 hours would be:
Horizontal distance = 330 km/hr × 2 hr = 660 km.
Step 2: Find the vertical distance covered by the plane.
The vertical component of the velocity of the plane is the same as its northward velocity, which is 400 km/hr.
Using the formula distance = speed × time, the vertical distance covered by the plane in 2 hours would be:
Vertical distance = 400 km/hr × 2 hr = 800 km.
Step 3: Apply the Pythagorean theorem to find the distance of the plane from its base.
According to the Pythagorean theorem, the distance of the plane from its base can be found by taking the square root of the sum of the squares of the horizontal distance and the vertical distance.
Distance = √(Horizontal distance^2 + Vertical distance^2)
Distance = √(660 km^2 + 800 km^2)
Distance = √(435600 km^2 + 640000 km^2)
Distance = √1075600 km^2
Distance ≈ 1037.68 km
Therefore, the distance of the plane from its base in 2 hours is approximately 1037.68 km.
To find the distance of the plane from its base in 2 hours, we can use the Pythagorean theorem. Here are the steps to get the answer:
Step 1: Determine the horizontal and vertical components of the plane's velocity.
The plane's velocity is given as 400 km/hr to the north. Since the wind is blowing from the west, we need to consider its impact on the plane's motion. The wind's velocity is given as 70 km/hr to the west.
The vertical component of the plane's velocity is 400 km/hr (north) since there is no wind blowing in that direction.
The horizontal component of the plane's velocity is the difference between the plane's velocity and the wind's velocity. So, it would be 400 km/hr (north) - 70 km/hr (west).
Step 2: Calculate the distances covered in the vertical and horizontal directions.
Since the plane is flying for 2 hours, we multiply the vertical component of the velocity (400 km/hr) by the time (2 hours) to find the distance covered in the vertical direction. Thus, the distance covered would be 400 km/hr * 2 hours.
Similarly, we multiply the horizontal component of the velocity (330 km/hr, calculated as 400 km/hr - 70 km/hr) by the time (2 hours) to find the distance covered in the horizontal direction. The distance covered would be 330 km/hr * 2 hours.
Step 3: Use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In our case, the distances covered in the vertical and horizontal directions represent the two sides of a right triangle, and the distance of the plane from its base represents the hypotenuse.
So, we calculate the distance of the plane from its base using the Pythagorean theorem:
Distance^2 = (vertical distance)^2 + (horizontal distance)^2
Step 4: Calculate the distance.
Taking the square root of both sides of the equation, we get:
Distance = sqrt((vertical distance)^2 + (horizontal distance)^2)
Substituting the values we found earlier, we can calculate the distance of the plane from its base.
I'll do the calculations:
Vertical distance = 400 km/hr * 2 hours = 800 km
Horizontal distance = 330 km/hr * 2 hours = 660 km
Distance = sqrt((800 km)^2 + (660 km)^2) = sqrt(640000 km^2 + 435600 km^2) = sqrt(1075600 km^2) = 1037.77 km
Therefore, the distance of the plane from its base in 2 hours is approximately 1037.77 km.