Answer to Question #147876 in Mechanics | Relativity for Eca

Question

An ambulance has successive displacements of 6.3km, 45 deg., 12km south; and 4.7 km, 30 deg. south
of west. a] Determine the magnitude and directionof the resultant displacement b].What is the total
distance traveled by the ambulance?

Answer 1

Let`s start to solve the problem by identifying given valuables:

S₁=6.3 km this is the first displacement,

and we have given some angles and displacements.

a) In this case, the graph of motion of ambulance should be given but it was not given us, therefore we will solve this problem by our imagination. Firstly, let`s consider that ambulance went to south with 6.3 km and it changes its direction to 45 degrees to west and it goes 12 km, lastly it changes its direction again to 30 degrees to south of west. After that it moved totally 17.13 km and 12.55 km to south and west respectively but it moved with15 degrees to west of south. We already found its direction and it is enough to compute its displacement:

S²=17.13²+12.55² by pifagor theorem

S=21.23 km it means that an ambulance moved 15 degrees to west of south with 21.23 km total displacements.

b) To find total displacements that ambulance travelled, we need to add all given displacements:

S=6.3+12+4.7=23km ambulance travelled to 23 km.