Projectile Problem - Bullet from Raised ground

[aatari]

Hi Guys, could someone kindly look at my solutions and let me know if I did everything correctly.
Thanks a lot!

1. Homework Statement
A sniper fires a bullet at 120 m/s at 30° above the horizontal from the roof top of a 35 m high parking garage. If the bullet strikes the level ground beside the parking garage:

1. How long was the bullet in the air?
2. How far from the base of the parking garage did the bullet land?
3. At what angle did the bullet land?

Homework Equations

d = v.t
d = vt+1/2at^2

The Attempt at a Solution

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[kuruman]

Parts (a) and (b) look good. Part (c) is incorrect. You need to use the components of the final velocity to find the angle.

 

[aatari]

Parts (a) and (b) look good. Part (c) is incorrect. You need to use the components of the final velocity to find the angle.

How do I find the final velocity?
Do I simply use v2 = v1 + a*t?

 

[kuruman]

Yes.

 

[aatari]

Yes.

one more question. Could I also use v2^2 = v1^2 +2*a*d?
What's the criteria to choose one equation over another?

 

[kuruman]

Could I also use v2^2 = v1^2 +2*a*d?

You could, but you have to choose the negative root because the bullet has a downward y-component when it hits the ground. The other equation allows to find the final y-component directly and its sign tells you whether the bullet is moving up or down.

 

[aatari]

You could, but you have to choose the negative root because the bullet has a downward y-component when it hits the ground. The other equation allows to find the final y-component directly and its sign tells you whether the bullet is moving up or down.

Ok so here is my solution.

V2 = v1 + a*t
= 60 -125 = -65

-65 m/s becomes my vertical component. Whereas 104 is my horizontal because horizontal remains constant.
Thereon I used tan-1 = O/A, which was 104/65. My final angle was 58 degrees

 

[TSny]

V2 = v1 + a*t
= 60 -125 = -65

-65 m/s becomes my vertical component. Whereas 104 is my horizontal because horizontal remains constant.

OK.

Thereon I used tan-1 = O/A, which was 104/65. My final angle was 58 degrees

Is this the angle as measured from the horizontal or as measured from the vertical?

 

[aatari]

OK.
Is this the angle as measured from the horizontal or as measured from the vertical?

I guess vertical?? Please see the diagram I drew. Pardon my not so great artistic abilities.

 

[scottdave]

If it was me, I would probably state the angle it makes with the horizontal, rather than vertical. That is the way you originally attempted the answer. The problem statement uses angle with horizontal, when stating the initial firing angle. So if you want to do that, find the angle which is complimentary to 58°

 

[aatari]

Thanks for all your help guys. Really appreciate it.