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39 problems tagged with relative motion
P0721
Intermediate Mechanics › KinematicsMinimum meeting time of two boats
Two boats on opposite sides of a river with width $d$. the line connecting the two boats is at an angle $\alpha$ with the river bank. The boats' speed is $v_1$ and $v_2$, respectively, and river flow speed is $u$. If they start rowing at the same time, what is the minimum time for them to meet and at what angle they should row the boat?
P0302
Intermediate Mechanics › KinematicsBoat Velocity in a River Current
A river of width $W$ flows due east at a uniform speed $v_w$. A boat with a speed $v_b$ relative to the water leaves the south bank pointed at an angle $\theta$ west of north.
- What is the magnitude of the boat's velocity relative to the ground, $v_{bg}$?
- What is the direction of the boat's velocity relative to the ground?
- How long, $t$, does the boat take to cross the river?
P0329
Advanced Mechanics › KinematicsCalculating Wind Velocity from Ship's Motion
A steamship is sailing due north at a speed of 15 km/h. A person on the ship observes the smoke from the smokestack drifting due east. Later, the ship sails due east at a speed of 24 km/h, and the person observes the smoke drifting due northwest. It is assumed that the wind velocity is constant during both journeys.
- Find the speed of the wind.
- Find the direction of the wind.
P0338
Advanced Mechanics › KinematicsKinematics of a Boat Pulled by a Rope
As shown in the diagram, a person on a pier of height $h$ above the water pulls a rope attached to a boat at point A. The person pulls the rope, causing it to be reeled in at a constant speed $V$.
- Find the speed of the small boat when the angle between the rope and the water surface is $\theta = 30^{\circ}$.
- Find the acceleration of the small boat when the angle between the rope and the water surface is $\theta = 30^{\circ}$.
P0237
Beginner Mechanics › KinematicsFerry Crossing a River Perpendicularly
A ferry crosses a river that is 600 m wide. The crossing takes 1.0 min and the ferry's resultant path is perpendicular to the river banks. The speed of the ferry in still water is 20 m/s.
- What is the speed of the river current?
- What is the angle between the boat's heading (velocity relative to water) and the direction of the current?
P0739
Intermediate Mechanics › KinematicsRelative Velocity of Wind and Runner
A person running due west at a speed of 2.5 m/s feels the wind coming from due north. If they double their speed, they feel the wind coming from the northwest.
P0741
Intermediate Mechanics › KinematicsProjectile Motion from a Circular Path
An ice skater skates on a circular path of radius $R = 15$ m at a constant speed $v_0 = 7$ m/s. They throw a ball horizontally from a height $h = 1.5$ m, aiming for it to land at the center of the circle.
- What is the required magnitude of the ball's velocity relative to the skater?
- What is the direction of this velocity, expressed as the angle $\theta$ with the skater's instantaneous velocity?
P0742
Intermediate Mechanics › KinematicsRelative Velocity of Rain and Train
A person observes rain streaks on a train window. Angles are measured from the vertical.
- When the train is stopped, the streaks are tilted forward at an angle $\theta_0$.
- When the train moves forward at a constant velocity $v_1$, the streaks are tilted backward at an angle $\theta_1$.
- When the train moves at a new constant velocity $v_2$, the streaks are tilted backward at an angle $\theta_2$.
P0746
Advanced Mechanics › KinematicsMotion of a stick on a ring
A very long stick AB is moving down with constant velocity on a fixed ring of radius $r$ centered at point O. At a moment, the stick intersects with the ring at point MN, and the angle $\angle MON = 2\phi$. Find the velocity and acceleration of intersection point M.
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