A man starts running a race with velocity v. in the begining of race he finds wind is blowing at an angle alpha with the track. As he progress straight horizontal road wind appears to rotate uniformly and by the gime he completes the race wind appears to rotate by an angle alpha. If the wind always blows perpendicular to the track and the time of race is t. What will be the following
1. Velocity of wind.
2. Is the speeding up or slowing down.
3. Is the motion of man uniform acceleartion or non uniformal acceleartion.
4. Length of the race.
To solve this problem, we can break it down into smaller steps:
Step 1: Find the velocity of the wind.
We know that the wind blows perpendicular to the track and appears to rotate by an angle alpha during the race. This means that the change in the wind's direction is equal to alpha. Since the wind rotates uniformly, we can calculate its velocity by dividing the change in angle by the time of the race:
Velocity of wind = alpha / t
Step 2: Determine if the man is speeding up or slowing down.
We know that the wind blows perpendicular to the track, which means it does not affect the man's velocity directly. However, the wind's rotation does impact the apparent direction the man feels. Since the wind appears to rotate by an angle alpha, the man would feel an apparent force that alters his direction. This force could either speed him up or slow him down depending on the direction of the rotation. Without knowing this information, we cannot determine if the man is speeding up or slowing down.
Step 3: Determine if the motion of the man is uniform acceleration or non-uniform acceleration.
Since we don't have any other information about the forces acting on the man, we cannot determine if his motion is uniform acceleration or non-uniform acceleration. This would require additional details about the forces involved.
Step 4: Calculate the length of the race.
To calculate the length of the race, we would need to know the man's initial velocity (v). If the motion is uniform (constant velocity), then we can use the formula:
Length of the race = Velocity of the man * time of the race = v * t
If the motion is non-uniform and we have additional details about the acceleration, we can use the appropriate kinematic equation to determine the length of the race. However, with the given information, we cannot determine the length of the race.
To find the answers to the questions, we can break down the problem and analyze it step by step:
1. Velocity of the wind:
Since the wind appears to rotate uniformly by an angle alpha from the beginning to the end of the race, and it always blows perpendicular to the track, we can consider the wind's motion as circular motion. The time it takes for the wind to rotate by an angle alpha is the same as the time it takes for the man to complete the race.
The angular speed is given by the formula:
angular speed (ω) = angle (alpha) / time (t)
The velocity of the wind can be calculated by multiplying its angular speed by the distance from the center of the circular track:
velocity of wind = angular speed (ω) * radius of the circular track
2. Speeding up or slowing down:
If the man is running in a straight horizontal road and the wind appears to rotate uniformly, it means that the wind's velocity remains constant throughout the race. Therefore, there is no speeding up or slowing down of the wind.
3. Motion of the man:
Since the man is running on a straight horizontal road without any change in velocity, his motion can be considered uniform motion. Uniform motion is characterized by a constant velocity.
4. Length of the race:
To determine the length of the race, we need to consider the distance the man covers while running. Since the motion of the man is considered uniform, we can use the formula:
distance (d) = velocity (v) * time (t)
where the velocity of the man (v) is given in the problem.