Projectile Motion

Question

A hiker makes four straight-line walks A= 28 km at 77 degrees B= 32 km at 296 degrees C= 24 km at 27 degrees D=19 km at 83 degrees in random directions and lengths starting at position (41 km, 41 km)How far from the starting point is the hiker after these four legs of the hike? All angles are measured in a counter-clockwise direction from the positive x-axis. Answer in units of km

Answer 1

To determine the final location, break each segment into an equivalent x-component and y-component. To do so, use the trig ratios sine and cosine:

A:

x-component = 28cos(77°) = 6.2986 km

y-component = 28sin(77°) = 27.2824 km

B:

x-component = 32cos(296°) = 14.0279 km

y-component = 32sin(296°) = -28.7614 km

C:

x-component = 24cos(27°) = 21.2842 km

y-component = 24sin(27°) = 10.8978 km

D:

x-component = 19cos(83°) = 2.3155 km

y-component = 19sin(83°) = 18.8584 km

Now, add all the x-components together and add all the y-components together:

x-component total = 6.2986 km + 14.0279 km + 21.2842 km + 2.3155 km = 44.0262 km

y-component total = 27.2824 km - 28.7614 km + 10.8978 km + 18.8584 km = 28.2751 km

Now, use the Pythagorean Theorem to find the resultant:

Resultant = √(44.0262² + 28.2751²) = √2737.7859 = 52.3 km

So the hiker is 52.3 km from his starting point