Question

Your directions on a scavenger hunt map say to walk 42 m east, then 35 m south, then 28 m 20° north of west. The positive x direction is the direction to the east and the positive y direction is the direction to the north. What are the magnitude and direction of your displacement?

Starting from rest, a cart takes 1.55 s to slide 1.90 m down an inclined frictionless track. What is the angle of incline of the track with respect to the horizontal?

Answer 1

1)

let A = 42 m
Ax = 42 m, Ay = 0
B = 35 m
Bx = 0, By = -35 m
C = 28 m
Cx = -28*cos(20) = -26.3 m
Cy = 28*sin(20) = 9.58 m

Rx = Ax + Bx + Cx

= 42 + 0 - 26.3

= 15.7 m

Ry = Ay + By + Cy
= 0 - 35 + 9.58

= -25.4 m

resultant displacement,
|R| = sqrt(Rx^2 + Ry^2)

= sqrt(15.7^2 + 25.4^2)

= 29.9 m

direction : theta = tan^-1(Ry/Rx)

= tan^-1(-25.4/15.7)

= 58.2 degrees south of east

2) let a is the acceleration.

use, d = (1/2)*a*t^2

==> a = 2*d/t^2

= 2*1.9/1.55^2

= 1.582 m/s^2

we know, a = g*sin(theta)

==> theta = sin^-1(a/g)

= sin^-1(1.582/9.8)

= 9.30 degrees