a man rides a motorcycle 12km due east and later 5km due north. calculate the:
1.total distance covered
2.displacement covered
start at (0 , 0)
go right to (12 , 0 )
go up to (12 , 5 )
draw it, right triangle, we want sum of perpendicular legs and then hypotenuse
12 + 5 for sum
sqrt ( 12^2 + 5^2 ) = sqrt (144+25) = sqrt (169) = 13
of course you knew that 5 , 12 , 13 was a right triangle anyway, right?
you are wrong fool i need a physics explanation of this
To calculate the total distance covered, you can 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 this case, the man first travels 12km due east and then 5km due north. These two distances form the sides of a right-angled triangle. The distance covered by the man is the hypotenuse of this triangle.
1. Total distance covered:
Using the Pythagorean theorem, you can calculate the total distance covered as follows:
Total distance = √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13 km
Therefore, the total distance covered by the man is 13 km.
2. Displacement covered:
Displacement refers to the straight-line distance from the starting point to the end point. It considers both the magnitude and direction of the motion.
To calculate the displacement, you can use the concept of vectors. The eastward distance is considered positive (+12km), while the northward distance is considered positive (+5km).
To find the displacement, you need to find the resultant vector of these two distances. The resultant vector is the sum of these two vectors, taking into account their direction.
To add these vectors, you can use the Pythagorean theorem again. Consider the eastward distance as the horizontal component and the northward distance as the vertical component. The displacement is the magnitude of the resultant vector, and the angle formed by the resultant vector with the east direction is the direction of displacement.
Using trigonometry, you can calculate the displacement as follows:
Displacement = √((12^2) + (5^2))
= √(144 + 25)
= √169
= 13 km
The magnitude of the displacement is 13 km, and to find the direction, you can use the inverse tangent function:
θ = tan^(-1) (5/12)
≈ 22.62 degrees
Therefore, the displacement covered by the man is 13 km in a direction approximately 22.62 degrees north of east.