Relative Motion – Fill-in-the-Blank Flashcards

50 fill-in-the-blank flashcards covering core formulas, conditions, and concepts of relative motion, river-boat, wind-airplane, and rain-umbrella problems.

Because motion is judged with respect to another body, it is called a __ concept.

relative

The symbol for the position vector of B with respect to A is __.

r_B/A

Differentiating rB = rA + rB/A gives vB = vA + ___.

v_B/A

Taking the second derivative yields aB = aA + __.

a_B/A

The relation vA/B = − ___ expresses that relative velocities are opposite.

v_B/A

Velocity of approach/separation is the component of relative velocity along the __ joining the particles.

line

If the separation between two bodies is decreasing, the component is called velocity of __.

approach

With zero relative acceleration, two particles collide when their relative velocity points __ one another.

towards

Separation is minimum when dS/dt equals __.

0

Shortest distance dshortest = |r12 × v12| / ___.

|v_12|

Minimum distance occurs when the line of centers is perpendicular to the __ velocity.

relative

Relative velocity of two equal-speed particles is maximum when the angle between their velocities is __ radians.

π

To minimise crossing time, a swimmer must aim __ to the river flow.

perpendicular

The minimum time to cross a river of width d with swim speed u is __.

d/u

For zero drift when u > vriver, the aiming condition is u sin θ = ___.

v_river

If swimmer speed is less than river speed, achieving zero drift is __.

impossible

Drift is minimised when the derivative of drift with respect to aim angle is set to __.

zero

Ground velocity of an aeroplane equals its air velocity __ the wind velocity.

plus

When an observer moves with speed vm, the rain’s apparent tilt satisfies tan θ = vm / __.

v_rain

An umbrella must be held against the direction of the rain’s __ velocity.

relative

To an observer on the truck, a ball thrown straight up follows a __ line.

vertical

To an observer on the ground, the same ball follows a __ path.

parabolic

Throwing a ball forward from a moving truck gives ground horizontal speed u cos θ __ truck speed.

plus

Throwing it backward gives ground horizontal speed u cos θ __ truck speed.

minus

Cross-river time equals width divided by the __ component of ground velocity.

perpendicular

For face protection, tan θ = (face length)/(hat overhang); hence maximum running speed satisfies tan θ = __ / L_hat.

L_face

If rain falls vertically at 10 m s⁻¹ and umbrella tilt is 53°, the walker’s horizontal speed is __ m/s.

4

Velocity addition: vm/g = vm/w + __.

v_w/g

On a round-trip A→B→A with wind, no drift requires the plane’s cross-wind air component to __ the wind.

cancel

Three mutually chasing particles meet at the triangle’s __.

centroid

For the chase, meeting time t = a / (v × __).

√3

For cars at 90° roads (20 m/s & 15 m/s), the relative speed magnitude is __ m/s.

25

Minimum distance occurs when relative position is perpendicular to __ velocity.

relative

Rain appears vertical to a stationary observer because horizontal relative velocity is __.

zero

Collision requires rAB and vAB to have the same __.

direction

Drift distance equals river speed multiplied by __.

crossing time

For straight-across travel, sin θ = vriver / ___.

u_boat

General rule: vobject/ground = vobject/medium + v___/ground.

medium

When rain falls vertically and walker moves horizontally, relative speed magnitude is √(vrain² + vwalk²) because directions are __.

perpendicular

Two equal-speed particles moving in opposite directions have __ relative velocity.

maximum

Upstream ground speed equals boat speed relative water __ river speed.

minus

Downstream ground speed equals boat speed relative water __ river speed.

plus

The minimum-time path across a river is __ than the minimum-drift path.

shorter

If both bodies share identical accelerations, their relative acceleration is __.

zero

With constant horizontal resistance, a projectile’s trajectory can remain __.

parabolic

In mutual chase on an equilateral triangle, velocity makes a constant 30° with the line to the __.

centroid

The first derivative of relative position with respect to time is called __.

relative velocity

The second derivative of relative position with respect to time is called __.

relative acceleration

In one dimension, the magnitude of relative velocity equals the __ of individual velocities.

difference

For perpendicular motions with speeds v₁ and v₂, relative speed magnitude is __.

√(v₁² + v₂²)