Solve problems involving relative velocity

Solve problems involving relative velocity

Relative Velocity Problem Solving

Case of Same Direction: When two objects are moving in the same direction, the relative velocity of object B with respect to object A is given by subtracting the velocity of A from the velocity of B (i.e., VB - VA).

Case of Opposite Direction: When two objects are moving in opposite directions, the relative velocity is calculated by adding the individual velocities of the two objects (i.e., VB + VA).

Case of Perpendicular Directions: If two objects are moving perpendicularly, use the Pythagorean theorem to calculate the relative velocity (√(VA²+VB²)).

Relative velocity in x-y plane: When the objects are not moving along the same line, resolve each object’s velocity into components along x and y axes. Calculate the relative velocity for each direction separately, i.e., Relative velocity in x-direction = VBx - VAx and Relative velocity in y-direction = VBy - VAy.

Use of Angles in Relative Velocity

Direction of Relative Velocity: When the objects are not moving along the same line, calculate the angle for the resultant relative velocity using trigonometric ratios.

Trigonometric Ratios: If θ is the angle with the positive x-axis and VRx, VRy are the components of relative velocity along x and y-axis respectively, tan(θ) = VRy / VRx. Ensure to consider the quadrant in which the resultant relative velocity lies for the correct angle.

Drag and Wind Velocity

Influence of Medium: Consider the effect of the medium on the relative velocity. For instance, the speed of a boat in a river will be affected by the river’s current, and the speed of an aircraft will be affected by the wind speed (wind is considered as ‘moving air’).

Wind/Current Speed: The resultant velocity of an object moving in wind or water (or any other medium in motion) parallelly is the vector sum of the object’s own speed and the speed of the medium. If these two are at an angle, use the rules of vector addition.

Worked Examples and Practice Problems

Thoroughly familiarise yourself with a broad range of examples where relative velocity is used to find either the relative speed or relative direction or both. This allows to understand the concept in different contexts, thus building proficiency in problem-solving.

Key Pointers and Revision Notes

Consistently review the formulas and methods used to calculate relative velocity. Pay particular attention to problems involving vectors as these can be slightly more complex. In all cases, ensure to understand the principles underpinning each solution to enhance mastery of the topic.