Answer :
Answer:
To solve this problem, we'll break it down into two components: the horizontal and vertical components of the plane's motion.
First, let's consider the horizontal motion:
For the first leg of the journey (at a bearing of 060°), the horizontal displacement (
1
d
1
) can be calculated using:
1
=
speed
×
time
d
1
=speed×time
1
=
150
mph
×
2.0
hours
=
300
miles
d
1
=150mph×2.0hours=300miles
For the second leg of the journey (at a bearing of 150°), the horizontal displacement (
2
d
2
) can also be calculated similarly:
2
=
speed
×
time
d
2
=speed×time
2
=
150
mph
×
3.0
hours
=
450
miles
d
2
=150mph×3.0hours=450miles
Now, let's consider the vertical motion:
Since the plane flies at a constant speed, there is no change in altitude, so the vertical displacement is zero.
Now, we'll use the Pythagorean theorem to find the total distance from the starting point, which is the hypotenuse of the right triangle formed by the horizontal and vertical displacements:
Total distance
=
1
2
+
2
2
Total distance=
d
1
2
+d
2
2
Total distance
=
30
0
2
+
45
0
2
Total distance=
300
2
+450
2
Total distance
=
90000
+
202500
Total distance=
90000+202500
Total distance
=
292500
Total distance=
292500
Total distance
≈
540.55
miles
Total distance≈540.55miles
So, at the end of this time, the plane is approximately
540.55
540.55 miles from its starting point.
Step-by-step explanation:
