Question

A hiker walks 4.5 km in one direction, then makes a 45-degree turn and walks another 3 km. What is the hiker's total displacement from the starting point?

a) 5.7 km
b) 6.4 km
c) 7.1 km
d) 8.2 km

Answer 1

The hiker's total displacement from the starting point is 5.4 km, which is closest to option a) 5.7 km.

Step-by-step explanation:

The hiker's displacement can be found by using the Pythagorean theorem. The distance walked in one direction is 4.5 km, and the distance walked after the turn is 3 km. To find the displacement, we can treat these distances as the legs of a right triangle. The displacement is then the hypotenuse of this triangle. Using the Pythagorean theorem, we can calculate the displacement:

Displacement = sqrt((4.5 km)^2 + (3 km)^2) = sqrt(20.25 km^2 + 9 km^2) = sqrt(29.25 km^2) = 5.4 km

Therefore, the hiker's total displacement from the starting point is 5.4 km, which is closest to option a) 5.7 km.