Question

A hiker travels 22.5 km at 45.0 degrees in 10.0 hrs on day one, 18.0 km at 75.0 degrees in 9.50 hours on the second day, and 13.0 km at 130.0 degrees in 7.50 hrs on the third day.

a) Find the resultant displacement, in magnitude and direction form, for the hiker.

b) Calculate the average speed the hiker has for the trip (don't take into account rest time).

c) Calculate the average velocity the hiker has for the trip (don't take into account rest time).

d) If the hiker traveled on a fourth day, what displacement must they make to have a resultant displacement displacement of 50.0 km at 90.0 degrees for all four day travel?

Answer 1

a.

First, let's define the displacement as vectors:

Then:

We can define resultan displacement as:

b.

Speed is a scalar magnitud, then

c.

Velocity is a vector magnitud, then:

d.

We can define total new displacement as follow:

Or, in other words: