Vectors|Please help!

Question

"Vector u has a magnitude of 15 and a direction of 0°. Vector v has a magnitude of 18 and a direction of 70°. Find the magnitude and direction of the resultant to the nearest whole number."

For this problem is used the formula (m)^2 = u^2 + v^2 - 2uv cos 110°, so

15^2 + 18^2 - 2(15)(18)cos 110°

which equaled 225 + 324 - 540 cos110°, and then I squared my equation, which got me ≈ 27

As for finding my direction, I used sin110/27 = sinθ/70 which equaled sinθ = sin110 x 70/27 and got ≈2.43...

But when I got the inverse of my answer on desmos, the answer was labeled as undefined.

Any help with finding the correct direction would be much appreciated.

Answer 1

You did a nice job with the magnitude. To get the direction of the resultant vector, you want to take the arctan(change in y/change in x) with respect to the resultant vector. The change in y = 15sin(0)+18sin(70) = 16.914. The change in x = 15cos(0)+18cos(70)=21.156. arctan(16.914/21.156) is approximately 39 degrees

Answer 2

desmos.com/3d/3drococnqp

Answer 3

"Vector u has a magnitude of 15 and a direction of 0°. Vector v has a magnitude of 18 and a direction of 70°. Find the magnitude and direction of the resultant to the nearest whole number." 

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First of all, review the math problem and then select the important facts.    

 

Remember to show work (Use the step-by-step approach)  

 

Set up the equation before using the Calculator 

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What are you solving for in the math problem?  

 

Find the magnitude and direction of the resultant vector of two given vectors. 

 

What information is given in the problem? 

 

Vector (u) has a magnitude of 15 and a direction of 0 degrees. 

 

Vector (v) has a magnitude of 18 and a direction of 70 degrees. 

 

Vital Information: 

 

The x component of a vector is given by ax = a cos (theta),  

where (a) is the magnitude and  

(Theta) the direction angle. 

 

The y component of a vector is given by ay = a sin (theta),  

where (a) is he magnitude and  

(Theta) the direction angle. 

 

The magnitude of the resultant vector r is given by absolute r = square root of (r^2x + r^2y), where rx and ry are the x and y components of r. 

 

The direction of the resultant vector r is given by theta = arctan (ry divided by rx) 

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Use the following information to solve the math problem: 

 

Step 1 

Find the x and y components of vector u 

ux = 15 cos (0 degrees) = 15 x 1 =15 

uy = 15 sin (0 degrees) = 15 x 0 = 0 

 

Step 2 

 

Find the x and y components of vector v 

 

vx = 18 cos (70 degrees) = 15 x 1 =15  = 18 x 0.342 = 6.156               cos(70) = 0.3420201433 

vy = 18 sin (70 degrees) =  15 x 0 = 0     = 18 x 0.940 = 16.92               sin (70) = 0.9396926208 

 

Step 3 

Find the x and y components of the resultant vector r. 

rx = ux + vx = 15 + 6.156 = 21.156 

ry = uy + vy = 0 + 16.92 = 16.92 

Step 4 

Absolute r = square root of (r^2x + r^2y) = square root of (21.156)^2 + (16.92)^2  

= square root of (447.57 ) + (286.29) = square root of (733.86) = 27.0898505 roundoff as specified =  27.1 

Step 5 

Calculate the direction of the resultant vector (r). 

 tan^-1 (0.7998) = 38.65282028 roundoff as specified 

Theta = arctan ry divided by rx = arctan (16.92 /21.156) = arctan (0.7998) =  

38.65282028 =  39 degrees 

 

Final Answer: 

The magnitude of the resultant vector is 27.1 = 27 

The direction is 38.6 = 39 degrees 

Hope that the information is helpful. Please contact me if you have any additional math questions or need further assistance in your academic study.