Tara Goes On A Camel Safari In Africa. She Travels 5 Km North, Then 3km East And Then 1km North Again. What Distance Did She Cover? What Was Her Displ

tara goes on a camel safari in africa. she travels 5 km north, then 3km east and then 1km north again. What distance did she cover? What was her displacement?

 

Let d represent as displacement.

Let R represent as resultant.

Let Φ represents as the angle.

Given:

d1 = 5 km, 90°

d2 = 3 km, 0°

d3 = 1 km, 90°

Formula:

For horizontal x-axis:

(n)(cosΦ)

For vertical y-axis:

(n)(sinΦ)

For the resultant (or the magnitude displacement):

R = √((x)^2 + (y)^2)

For the angle (althought unnecessary):

Φ = arctan (y/x)

Equation:

d1x = (5 km)(cos90) = 0 km

d1y = (5 km)(sin90) = 5 km

d2x = (3 km)(cos0) = 3 km

d2y = (3 km)(sin0) = 0 km

d3x = (1 km)(cos90) = 0 km

d3y = (1 km)(sin90) = 1 km

Summation of dx = (d1 + d2 + d3)x = 3 km

Summation of dy = (d1 + d2 + d3)y = 6 km

R = 3√5 km or 6.708203932 km

Φ = 63.43494882°

Answer:

The displacement is approximately 6.71 km (or 7 km) at an angle of 63.43°.