Vector c has a magnitude 24.6 m and is in the direction of the negative y-axis. vectors a and b are at angles î± = 41.4â° and î² = 27.7â° up from the x-axis respectively. if the vector sum a b c = 0, what are the magnitudes of a and b?

The vector c has a magnitude of 24.6m and it is in the negative y direction. Therefore


The vector b is 41.4° up from the x-axis. Therefore


The vector a is 27.7° up from the x-axis. Therefore


Because , the sum of the x and y components should be zero. Therefore,
For the x-component,
0.8854a + 0.75b = 0
 or
 a + 0.847b = 0                            (1)
For the y-component,
0.4648a + 0.6613b - 24.6 = 0
 or
 a + 1.4228b = 52.926                (2)

Subtract (1) from (2).
0.5758b = 52.926
b = 91.917
a = -0.847b = -77.854

The magnitude of vector a is -77.85 m
The magnitude of vector b is 91.92 m

The objects do not reach terminal velocity         there is not enough time from the time the object falls from when it hits the ground to achieve terminal velocity. an object must be placed higher to achieve terminal velocity in order to be in free fall.