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Erica is participating in a road race. The first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25∘ north of east. The road then turns due north for another 6.0 mi to the finish line.

In miles, what is the straight-line distance from the starting point to the end of the race?

Sagot :

The distance between the starting point(initial) and the ending point(last) is known as displacement is  9.46miles.

What is displacement?

  • Displacement is defined as the change in position of an object. It's a vector volume and has a direction and magnitude. It's represented as an arrow that points from the starting position to the final position.
  • For illustration- If an object moves from A position to B, also the object's position changes.
  • Distance is a scalar volume that refers to" how important ground an object has covered" during its stir. Displacement is a vector volume that refers to" how far out of place an object is" it's the object's overall change in position.
  • Displacement is a defense medium that involves an individual transferring negative heartstrings from one person or thing to another.

In the first(1st) part of the race displacement of Erica is

d1 = 5.2 miles at 25(twenty-five) deg North of East

x(ax) and y-component of 1st(first) part of the race will be:

d1 = 5.2*cos 25(twenty five) deg i + 5.2*sin 25(twenty five) deg j

d1 = (4.71 i + 2.20 j) miles (this id d1)

In the second(2nd) part of the race

d2 = 6(six) miles towards north,

So

d2 = (6 j) miles (this is d2)

Now net(accurate) displacement of Erica will be, Using Vector addition(summation):

d = d1(4.71 i + 2.20 j) + d2(6j)

d = (4.71 i + 2.20 j) +(sum) (6 j)

d = 4.71 i +(sum) 8.20 j

So Magnitude of net(accurate) displacement will be:

|d| = [tex]\sqrt{4.71^2+8.20^2}[/tex]

|d| = 9.46 miles(nine.four-six) = distance between starting(initial) point and ending point

Learn more about displacement here: https://brainly.com/question/14422259

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