Vector Review Problem. Calculate the vector sum (i.e, the resultant ) for the fo

Question

Vector Review Problem. Calculate the vector sum (i.e, the resultant) for the following two velocity vectors: (15.0 m/s at 15.0°) + (6.00 m/s at 24.0°) The angles are given with respect to the positive x axis.
HINTS: You'll want to begin by calculating the x and y components of the two individual velocity vectors. Then answer the following questions about the resultant sum of the two vectors.

x component of the resultant: _________ m/s
y component of the resultant:__________ m/s

Magnitude of resultant (Units must be included):  

Direction: ______________°
Please find your angle by measuring in the counterclockwise direction from the positive x axis.

Explanation / Answer

here V1 = 15 m/s V2 = 6 m/s Q1 = 15o   Q2 = 24o

(V1)x =V1 cosQ1

= 15 x cos(15o) = 14.488 m/s

(V1)y = V1 sinQ1

= 15 x sin(15o) = 3.882 m/s

(V2)x = V2 cosQ2

= 6 x cos(24o) = 5.4812 m/s

(V2)y = V2 sinQ2

= 6 x sin(24o) = 2.4404 m/s

so the x component of the resultant is

Vx = (V1)x + (V2)x

= 14.488 + 5.4812 = 19.9692 m/s Ans

the y component of the resultant is

Vy = (V1)y + (V2)y

= 3.882 + 2.4404 = 6.3224 m/s Ans

so the magnitude of resultant is

V2 = (Vx)2 + (Vy)2

= (19.9692)2 + (6.3224)2 = 438.7416

V = 20.9461 m/s Ans

the direction of resultant

tanQ = Vy / Vx

tanQ = 6.3224 / 19.9692

Q = 17.56o   Ans

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