Question

Item 4 To be able to add and subtract vectors using geometric and vector addition. A brother and sister are playing in the woods, when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled di 24.0 m at 01 26.5° from the tree then turned and traveled d2 11.5 m at 02 131°. Meanwhile, the sister traveled d3 18.5 n at an angle of 63-114° from the tree. The angles are given with respect to east with counterclockwise being defined as positive Next Figure K2 of 2 Figure Boy Tree

Answer 1

Answers;

let a horizontal line parallel to X-Axis be drawn at the tip of d1.

Angle between the vector and the line = 180 - 26.5 = 153.5

Angle between the line and the boy = $\theta$2 = 131

So total angle between the 2 vectors = $\theta$ = 131 + 153.5 = 284.5 degrees

Resultant = R = sqrt( P^2 + Q^2 + 2*P*Q*cos $\theta$ )

R = sqrt ( 24^2 + 11.5^2 + 2*24*11.5*cos284.5 )

= sqrt ( 846.4597)

= 29.094 m (Answer)

Let the horizontal distance between O and d1 be y

d1 * cos($\theta$1) = y

y = 24 * cos (26.5)

= 21.478 m

Again horizontal distance between d2 and d1

= d2*sin ( 131 - 90)

= 11.5 * sin 41

= 7.545 m

Difference = 13.934 m

If the angle between base and resultant is x

cos (x) = 13.934 / 29.094

= 0.4789

x = 61.385 degrees ( Answer)