A boy moves 10km eastwards, 5km northwards and then 2km eastwards. The distance and magnitude of displacement of the boy is
net north 5Km
net East 12 Km
distance=sum=17km
displacement: sqrt(5^2+12^2) in direction arc tan (5/12) E of N
To find the distance traveled by the boy, you can simply add up the distances traveled in each direction. The boy moves 10 km eastwards, then 5 km northwards, and finally 2 km eastwards. Adding these distances gives:
10 km + 5 km + 2 km = 17 km
So, the distance traveled by the boy is 17 km.
To find the magnitude of displacement, we need to find the straight-line distance between the starting point and the ending point. To do this, we can use the Pythagorean theorem.
The boy moves 10 km eastwards and then 2 km eastwards, so the total eastward displacement is 10 km + 2 km = 12 km.
The boy also moves 5 km northwards, so the northward displacement is 5 km.
Now, we can use the Pythagorean theorem to find the magnitude of displacement. The displacement is the hypotenuse of a right triangle, with the eastward displacement as the base and the northward displacement as the height.
Using the Pythagorean theorem:
Magnitude of displacement = √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13
So, the magnitude of displacement of the boy is 13 km.
To find the distance traveled by the boy, we need to calculate the total path length.
1. From the starting point, the boy moves 10km eastwards.
2. Then, the boy moves 5km northwards.
3. Finally, the boy moves 2km eastwards.
To find the magnitude of displacement, we need to calculate the straight-line distance between the starting point and ending point.
Let's calculate the distance traveled by the boy first:
Path length = 10km + 5km + 2km = 17km
The distance traveled by the boy is 17km.
Now let's calculate the magnitude of displacement:
To find the magnitude of displacement, we need to find the straight-line distance between the starting point and ending point. This is equivalent to finding the hypotenuse of a right-angled triangle.
Using the Pythagorean theorem:
Distance traveled eastwards = 10km + 2km = 12km
Distance traveled northwards = 5km
Displacement = √((12km)^2 + (5km)^2)
Displacement = √(144km^2 + 25km^2)
Displacement = √(169km^2)
Displacement = 13km
The magnitude of displacement of the boy is 13km.