← Components and relative motion

Relative velocity, opposite directions

A car at 34 m/s follows a car at 28 m/s, moving the same way. Enter their relative velocity in m/s.

Two trains approach each other on parallel tracks, one at 30 m/s, the other at 25 m/s. From either cab, the other train closes alarmingly fast. How fast?

To calculate the relative velocity of two objects moving toward each other along a line, add the speeds.

30 m/s + 25 m/s = 55 m/s

one train: 30 m/sthe other train: 25 m/s
Toward each other: both motions shrink the gap, so each driver measures the sum, 55 m/s.

Each driver measures the other train approaching at 55 m/s. Both motions shrink the gap, so their effects add.

Set the two rules side by side. Two objects moving the same way partly cancel, so subtract. Two objects moving toward each other both shrink the gap, so add.

Two trucks drive toward each other on a straight road, one at 24 m/s, the other at 19 m/s. Calculate their relative velocity.

Write down the values in the question:

first truck = 24 m/s

second truck = 19 m/s, toward the first

relative velocity = ?

Write down the equation:

relative velocity = one speed + the other speed

Substitute in the values:

relative velocity = 24 m/s + 19 m/s

Simplify:

relative velocity = 43 m/s, closing

Two cyclists ride toward each other on a trail, one at 6.5 m/s, the other at 4.5 m/s. Calculate their relative velocity.

Write down the values in the question:

first cyclist = 6.5 m/s

second cyclist = 4.5 m/s, toward the first

relative velocity = ?

Write down the equation:

relative velocity = one speed + the other speed

Substitute in the values:

relative velocity = 6.5 m/s + 4.5 m/s

Simplify:

relative velocity = 11 m/s, closing

Now make the move quick. Six items follow: the objects move toward each other, so add.

Two cars drive toward each other, one at 22 m/s, the other at 16 m/s. Enter their relative velocity in m/s.

Two cyclists ride toward each other, one at 7.5 m/s, the other at 4.5 m/s. Enter their relative velocity in m/s.

Two trains head toward each other on parallel tracks, one at 44 m/s, the other at 31 m/s. Enter their relative velocity in m/s.

Two runners approach each other on a track, one at 5.5 m/s, the other at 3.5 m/s. Enter their relative velocity in m/s.

Two boats motor toward each other on a bay, one at 6.0 m/s, the other at 8.5 m/s. Enter their relative velocity in m/s.

A walker at 1.5 m/s and a jogger at 3.5 m/s approach each other on a path. Enter their relative velocity in m/s.

Your turn

Two planes fly head-on on one airway, one at 230 m/s, the other at 210 m/s. Enter their relative velocity in m/s.

A skydiver falls straight down at 48 m/s while a hot-air balloon directly below rises straight up at 4 m/s. Enter their relative velocity in m/s.

Two city buses drive toward each other on a straight street, one at 13 m/s, the other at 8 m/s. Enter their relative velocity in m/s.