1.A car is traveling a road that includes two sides of an equilateral triangle with a constant speed s. What is the magnitude of the average velocity v of the car?
2.A ship crosses a river aiming at the angle theta to the left from the straight courses. The speed of the ship with respect to water is v' . The width of the river is d. What is the water speed u ( positive direction to the right), if the side displacement of the ship as it lands on the other shore is
Time spent in motion = 2a/v
Displacement from starting point = a
Avg velocity = a/(2a/v) = v/2
Your second question is incomplete.
1. To find the magnitude of the average velocity of the car, we need to determine the total displacement and the total time taken.
The car is traveling along two sides of an equilateral triangle, so the total displacement would be equal to the sum of the lengths of these two sides. Let's call the length of each side "d". Since it is an equilateral triangle, the total displacement would be 2d.
To calculate the total time taken, we need to know the length of time the car traveled along each side of the triangle. Let's call this time "t". Since the car is traveling at a constant speed "s", the total time taken would be equal to twice the time it takes to travel one side of the triangle. Thus, the total time taken would be 2t.
Now, we can calculate the average velocity (v) using the equation:
v = displacement / time = (2d) / (2t) = d / t
Therefore, the magnitude of the average velocity of the car would be d / t.
2. To find the water speed (u) of the ship, we need to consider the velocity components in the horizontal (x) and vertical (y) directions.
Let's assume the speed of the ship with respect to land is "v" and the angle it aims to the left from the straight course is represented by "θ".
The x-component of the ship's velocity (u*cosθ) represents the velocity in the horizontal direction (positive direction to the right), and the y-component (u*sinθ) represents the velocity in the vertical direction (upward is conventionally considered positive).
The side displacement of the ship as it lands on the other shore can be considered as the horizontal component of velocity multiplied by time (d = u*cosθ * t).
From this equation, we can rearrange it to solve for u:
u = d / (t * cosθ)
Therefore, to determine the water speed of the ship (u), you need to know the side displacement (d), the time spent crossing the river (t), and the angle (θ) at which the ship aims from the straight course.