A student bikes to school by traveling first d_N = 0.900\rm {miles} north, then d_W = 0.600\rm {miles} west, and finally d_S = 0.100\rm {miles} south.
If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance d_b would the bird cover?
north .9 - .1 = .8
west .6
right triangle beacuse north is perpendicular to west
c^2 = a^2 + b^2
c^2 = .8^2 + .6^2
3,4 ,5 triangle = 2 (.3 , .4 , .5)
so answer is 1
or do it out
.8^2 = .64
.6^2 = .36
sum is 1
sqrt (1) = 1
To find the net displacement of the student, we can calculate the total distance traveled in the north direction and the total distance traveled in the south direction, and then subtract the latter from the former.
1. Convert distances to the same unit:
d_N = 0.900 miles
d_W = 0.600 miles
d_S = 0.100 miles
2. Calculate the net displacement in the north direction:
Net displacement in the north direction = d_N - d_S
= 0.900 miles - 0.100 miles
= 0.800 miles north
3. Calculate the net displacement in the west direction:
Net displacement in the west direction = d_W - 0
= 0.600 miles west
Therefore, the student's net displacement is 0.800 miles north and 0.600 miles west.
To find the total distance the student biked, we need to calculate the resultant vector by summing up the individual distances traveled in each direction.
Step 1: Convert all the distances into a vector format.
- The distance north, d_N, can be represented as a vector (0, d_N), where the first component represents the distance traveled east/west (in this case, 0), and the second component represents the distance traveled north/south.
- Similarly, the distance west, d_W, can be represented as a vector (-d_W, 0).
- The distance south, d_S, can be represented as a vector (0, -d_S).
Step 2: Add up the individual vectors to get the resultant vector.
To do this, add the corresponding components of the vectors together:
Resultant vector = (0, d_N) + (-d_W, 0) + (0, -d_S).
Adding the components together:
Resultant vector = (0 + (-d_W) + 0, d_N + 0 + (-d_S)) = (-d_W, d_N - d_S).
Step 3: Calculate the magnitude (or length) of the resultant vector.
The magnitude of a two-dimensional vector can be calculated using the Pythagorean theorem:
Magnitude = sqrt((-d_W)^2 + (d_N - d_S)^2).
Plugging in the values:
Magnitude = sqrt(d_W^2 + (d_N - d_S)^2).
Step 4: Substitute the given values to find the total distance.
Magnitude = sqrt(0.6^2 + (0.9 - 0.1)^2) = sqrt(0.36 + 0.64) = sqrt(1).
Therefore, the total distance the student biked is 1 mile.