Projectile Motion

Question

A hiker makes four straight-line walks

A 21 km at 269 ◦ B 12 km at 155 ◦

C 23 km at 33 ◦

D 21 km at 161 ◦

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.

How high is the tallest spot in the ball’s path? Answer in units of m.

Answer 1

Hi Charlie P.,

Let vector V = A + B + C + D

A = 21*cos(269) i + 21*sin(269) j

B = 12*cos(155) i + 12*sin(155) j

C = 23*cos(33) i + 23*sin(33) j

D = 21*cos(161) i + 21*sin(161) j

V = -11.808661 i + 3.438247 j

The magnitude of the vector is the distance from the starting point.

|V| = √(11.808661² + 3.438247²) = 12.3 km

I hope this helps, Joe.