Answer:
a) see attached figure.
b) The magnitude of Kevin´s overall displacement is 77.5 m.
The direction of the overall displacement is 11.2° north of east.
Explanation:
Please, see the attached figure for a better understanding of the problem.
The resultant overall displacement will be the sum of the vectors A+B (see figure).
The vector A is horizontal, it has no vertical component. Then:
A = (50.0 m, 0)
The vector B, in change, has a vertical and horizontal component. Applying trigonometry of right triangles we can find the components of B:
By trigonometry:
cos θ = adjacent / hypotenuse
sin θ = opposite / hypotenuse
In this case:
cos 30° = x-component of B / magnitude of B
cos 30° = x-B / 30.0 m
30.0 m · cos 30° = x-B
x-B = 26.0 m
sin 30° = y-component of B / 30.0 m
30.0 m · sin 30° = y-B
y-B = 15.0 m
Then, the vector B will be:
B = (26.0 m, 15.0m)
The overall displacement will be:
R = A + B
R = (50.0 m, 0) + (26.0 m, 15.0 m)
R = (50.0 m + 26.0, 0 + 15.0 m)
R = (76 m, 15 m)
The magnitude of the overall displacement will be:
[tex]|R| = \sqrt{(76 m)^{2} + (15 m)^{2}} = 77.5 m[/tex]
The magnitude will be 77.5 m.
Using trigonometry, we can find its direction (see figure):
cos θ = 76 m / magnitude of R
θ = 11.2°
The direction of the overall displacement is 11.2° north of east.
