Question

A bullet is fired at 32 degrees with respect to the horizontal. If the speed at which the projectile leaves the gun is 300 m/s find the magnitude of the horizontal and the vertical components of the bullet's initial velocity .

Answer 1

The initial velocity is 300 m/s on the hypotenuse of a triangle with an angle of 32 degrees above the horizontal. Draw a triangle and use this information along with the sin and cos functions to find the initial vertical and horizontal velocities. Do you know how to use sin and cos?

Answer 2

Sin is opposite over hypotenuse
Cos=adj/ hypotenuse .

But how am I supposed to use them if I don't have another value ?

Answer 3

Yes that is correct. The answer comes from this equation: sin(angle)=opposite/hypotenuse. So you solve for the opposite and get hypotenuse*sin(angle)=opposite and you can get the opposite side's value

Answer 4

So to put it in your calculator put 300*sin(32) and that will give you your answer and similarly with cos to find the adjacent

Answer 5

Ohkayyyy, I think I got it ,
So I have to set up like a cross multiplication type thing right?
Sin 32/ 1=a/300

So, a=(sin32) (300)?

Answer 6

No it isn't really cross multiplication. Look at this link and look at the first triangle on the right. http://en.wikipedia.org/wiki/Trigonometric_functions This is how you would set up your triangle in this problem with h=300, and the angle A=32. The functions you typed in for sin and cos are correct but remember when solving this you are taking the sin and cos of an angle to get opp/hyp or adj/hyp.

Answer 7

Ill set up the eq's for you to see if its more clear. So you know length h and angle A. Now to find length b you would use the equation cos(A)=b/h and multiply both sides by h to get h*cos(A)=b. Now plug in your numbers and get 300*cos(32) and you get length b, or your horizontal initial velocity

Answer 8

What is b in the equation? the Adjacent leg or the opposite leg?

Answer 9

The adjacent leg

Answer 10

And for the future, jsut remember: If you have a 2-dimensional vector 'v' with length 'a' and angle 'φ' between the vector and the X-axis, the vector always is:\[v = \left(\begin{matrix}a \cos(\phi) \\ a \sin(\phi)\end{matrix}\right)\]You'll need this all_the_time ;)

Answer 11

b=cos(32)/300?

And @MuH4hA
Alright, thanks (:

Answer 12

b=cos(32)*300. Remember you have to multiply the h in b/h=cos(32) to make it go to the other side

Answer 13

FML. -_-
I'm stupid. Okay, so 254.4?

Answer 14

Yeah thats right. Now find the vertical

Answer 15

Would that be the Pythagorean theorem?

Answer 16

yes either that or use h*sin(angle)=a

Answer 17

once you get the hang of it its easiest to just use the sin and cos functions because they are exactly the same except the sin and cos (if that makes sense)

Answer 18

I'm getting huge numbers .
a^2+64719.36=90000?

Answer 19

Use the sin function

Answer 20

158.99?

Answer 21

Yes

Answer 22

Ahhhhhhh!!! :D thank you SO MUCH.

Answer 23

No problem. Good luck