a boy runs 100m along the east,then he turns to his left side at right angle and runs for 50m along the north direction.find the distance and the magnitude of the displacement .
To find the distance and magnitude of the displacement, we can use the Pythagorean theorem.
Distance: The distance is the total length traveled by the boy. We can calculate it by adding the lengths of the two sides of the right triangle formed by the run along the east and the run along the north.
Distance = √(100^2 + 50^2) = √(10,000 + 2,500) = √12,500 = 111.8 meters (rounded to one decimal place)
Magnitude of Displacement: The magnitude of displacement is a straight line distance from the starting point to the final position of the boy. It can be calculated using the Pythagorean theorem as well.
Magnitude of Displacement = √(100^2 + 50^2) = √(10,000 + 2,500) = √12,500 = 111.8 meters (rounded to one decimal place)
Therefore, the distance traveled by the boy is 111.8 meters, and the magnitude of displacement is also 111.8 meters.
To find the distance traveled, we can calculate the total distance covered by the boy along the east direction and the north direction separately, and then add them up.
Distance traveled along the east direction = 100 meters
Distance traveled along the north direction = 50 meters
Total distance = Distance traveled along the east direction + Distance traveled along the north direction
= 100 meters + 50 meters
= 150 meters
Therefore, the total distance covered by the boy is 150 meters.
To find the magnitude of the displacement, we can consider the boy's final position relative to his initial position. Since he initially moves 100m east and then 50m north, we can calculate the displacement using the Pythagorean theorem.
Displacement (d) = √((East distance)^2 + (North distance)^2)
East distance = 100 meters
North distance = 50 meters
Displacement (d) = √((100 meters)^2 + (50 meters)^2)
= √(10000 square meters + 2500 square meters)
= √(12500 square meters)
≈ 111.8 meters
Therefore, the magnitude of the displacement is approximately 111.8 meters.
Let
x-axis => due east
y-axis => due north
then
100m due east and 50m due north
=>
New position P(100,50)
distance by Pythagoras, D=sqrt(100^2+50^2)
angle (from x-axis)= tan-1(y/x)=tan-1(50/100)=tan-1(1/2) [ in the first quadrant]