The question is incomplete! The complete question along with answer and explanation is provided below.
Question:
A student bikes to school by traveling first 1.00 miles north, then 0.500 miles west and finally 0.200 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 db would the bird cover
Given Information:
distance towards north = dn = 1.00 mi
distance towards west = dw = 0.500 mi
distance towards south = ds = 0.200 mi
Required Information:
distance covered by bird = db = ?
Answer:
distance covered by bird = 0.94 miles
Explanation:
As you can see in the attached image, by applying the Pythagoras theorem,
db = √(dn - ds)² + dw²
db = √ (1.0 - 0.20)² + 0.50²
db = √ 0.80² + 0.50²
db = 0.94 miles
Therefore, the bird would cover a distance of 0.94 miles
The question is incomplete. The following is the complete question.
A student bikes to school by traveling first dn = 1.00 miles north, then dw = 0.500 miles west and finally ds = 0.200 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 dB would the bird cover?
Answer: dB = 0.9435 miles
Explanation: Let's assume north as positive y-axis and east as positive x-axis. So, the components of the movement vectors are:
dn = + 1.00
dw = - 0.500
ds = - 0.200
As dn and ds are vetor pointing in opposite direction and dw, db and dn - ds make a triangle, with db being the hypotenuse:
db = [tex]\sqrt{(dn - ds)^{2} + dw^{2} }[/tex]
db = [tex]\sqrt{(1 - 0.2)^{2} +(- 0.5)^{2} }[/tex]
db = [tex]\sqrt{0.8^{2} + 0.25 }[/tex]
db = 0.9435
The distance the bird cover in a straight line is 0.9435 miles.
The vectors from this question is demonstrated in the attachment.
