Relative Motion Practice Problems
Problem 1.
An Olympic canoeist, capable of travelling at a speed of 4.5 m/s in still water, is crossing
a river that is flowing with a velocity of 3.2 m/s [E]. The river is 220 m wide.
1. If the canoe is aimed northward (directly across the river), what will its velocity
be relative to the shore?
2. How long will it take to cross the lake?
3. Where is the landing position of the canoe, relative to its original position?
4. At what angle should the canoeist aim in order to land directly across the river?
Problem 2
The airspeed of a small plane is 215 km/h. The wind is blowing at 57 km/h from the west.
Determine the velocity of the plane with respect to the ground if the pilot keeps the plane
aimed at a direction of [34° E of N]?
Problem 3
A fighter jet flying directly north at a speed of 400 mi/hr fires a missile 35o S of E at 600
mi/hr. What is the speed of the missile relative to the fighter jet..
Problem 1 Solution
It is always helpful to make a sketch of the problem.
As you can see,
and
form a right angled triangle with
as the
hypotenuse. We can use the Pythagorean Theorem to find the velocity of the boat
relative to the shore.
Since we are dealing with vectors, we also need to find the direction of
.
Problem 2 Solution
1.
The time it takes for the canoeist to cross the river is dependent on the vertical
component of its velocity only (
). The distance is must cross is in the vertical
axis, the distance it moves horizontally has no effect.
Therefore, the canoeist takes 49 s to cross the river.
2.
We can use the time we just calculated along with the horizontal velocity (
to find the horizontal displacement.
Therefore, the canoeist will land 156.5 m [E] of where he left the shore.
3.
)
This question requires a new sketch.
As you can see, the right-angled triangle has changed so that
hypotenuse and
is now the vertical component.
We are looking for
and know
is now the
(we know the magnitude and are looking
for the direction) and
. We can use
canoeist should launch at.
to find the angle the
Therefore, the canoeist should aim 45° W of N in order to travel straight across
the river.
Solution
Note that the wind is blowing from the west, which means it is pointing towards the east.
Since both velocities were given in kilometers per hour we can leave them and find an
answer that is also in kilometers per hour.
This is a basic vector addition question and can be solved using and components or
sine and cosine law. This solution will use components.
Solution
Note that the wind is blowing from the west, which means it is pointing towards the east.
Since both velocities were given in kilometers per hour we can leave them and find an
answer that is also in kilometers per hour.
This is a basic vector addition question and can be solved using and components or
sine and cosine law. This solution will use components.
Solution
This question has an extra step. We must use displacement and time to find groundspeed.
Once again, I will use and components to solve this problem. Feel free to try it using
the other method.
Note that we subtracted windspeed from groundspeed to find airspeed.