Question

Сани спустились под углом 45 градусов к горизонту с горы длиной 100 м . Определите проекции перемещения саней по вертикальному и горизонтальному направления.

Answer 1

Дано
S=100м
α=45°
Найти Sx и Sy
Sx=Scosα=100*cos45°=100√2/2=50√2
Sy=Ssinα=100*sin45°=100√2/2=50√2

Answer 2

Calculation of Projections of Sled Displacement

To determine the projections of the sled's displacement in the vertical and horizontal directions, we can use trigonometry. Given that the sled descended at an angle of 45 degrees to the horizon from a mountain with a length of 100 meters, we can calculate the projections as follows:

Let Sx be the horizontal displacement and Sy be the vertical displacement.

Using trigonometric functions, we can calculate the projections as follows:

Sx = S * cos(θ) Sy = S * sin(θ)

Where: - S is the length of the mountain (100 meters in this case). - θ is the angle of descent (45 degrees in this case).

Substituting the values into the formulas, we get:

Sx = 100 * cos(45) Sy = 100 * sin(45)

Calculating the values:

Sx = 100 * 0.7071 = 70.71 meters Sy = 100 * 0.7071 = 70.71 meters

Therefore, the horizontal projection of the sled's displacement is approximately 70.71 meters, and the vertical projection is also approximately 70.71 meters.