Question

Два велосипедисти починають рух з однієї точки та майже відразу набирають швидкості 3 і 4 м/с відповідно. Якою буде відстань між велосипедистами через … 1 хв після початку руху, якщо велосипе дисти рухаються: а) в одному напрямку; б) перпендикулярно один до одного?

Answer 1

Ответ:

а)  S = (v2 -v1) * t = (4 - 3) * 60 = 60 м

б) S = $\sqrt{(v1*t)^{2} + (v2*t)^{2} } = t * \sqrt{(v1)^{2} + (v2)^{2} } = 60 * \sqrt{9 + 16} = 300$ м

Answer 2

Calculation of Distance between Cyclists

To calculate the distance between the two cyclists, we need to consider their initial positions and the speeds at which they are moving. Let's analyze the two scenarios separately:

a) When the cyclists are moving in the same direction:

In this case, we can assume that one cyclist is ahead of the other. Let's call the cyclist in front "Cyclist A" and the cyclist behind "Cyclist B". Both cyclists start from the same point and begin moving with speeds of 3 m/s and 4 m/s, respectively.

After 1 minute (60 seconds), Cyclist A will have traveled a distance of 3 * 60 = 180 meters, and Cyclist B will have traveled a distance of 4 * 60 = 240 meters. The distance between them will be the difference between their positions, which is 240 - 180 = 60 meters.

b) When the cyclists are moving perpendicular to each other:

In this case, one cyclist is moving in the x-direction, and the other cyclist is moving in the y-direction. Let's call the cyclist moving in the x-direction "Cyclist A" and the cyclist moving in the y-direction "Cyclist B". Both cyclists start from the same point and begin moving with speeds of 3 m/s and 4 m/s, respectively.

After 1 minute (60 seconds), Cyclist A will have traveled a distance of 3 * 60 = 180 meters in the x-direction. Cyclist B will have traveled a distance of 4 * 60 = 240 meters in the y-direction. Since they are moving perpendicular to each other, the distance between them can be calculated using the Pythagorean theorem.

The distance between the two cyclists after 1 minute can be calculated as follows:

Distance = √((Distance traveled by Cyclist A)^2 + (Distance traveled by Cyclist B)^2)

Distance = √((180)^2 + (240)^2) = √(32400 + 57600) = √90000 = 300 meters

Therefore, the distance between the two cyclists after 1 minute will be 300 meters when they are moving perpendicular to each other.

Please note that the calculations provided above are based on the assumption that the cyclists maintain a constant speed and travel in a straight line. Additionally, the calculations assume that the cyclists start from the same point at the same time.