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Any Physics Buffs Around?

A

agahnim

Member
I'm having trouble solving this problem.

An arrow is shot at an angle of 45 degrees above the horizontal. The arrow hits a tree a horizontal distance of D = 220 meters away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity g = 9.8.

Find ta, the time that the arrow spends in the air.

Suppose someone drops an apple from a vertical distance of 6.0 meters , directly above the point where the arrow hits the tree.

How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Find td.

Any suggestions? Thanks for any reply
 
Originally posted by: agahnim
I'm having trouble solving this problem.

An arrow is shot at an angle of 45 degrees above the horizontal. The arrow hits a tree a horizontal distance of D = 220 meters away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity g = 9.8.

Find ta, the time that the arrow spends in the air.

Suppose someone drops an apple from a vertical distance of 6.0 meters , directly above the point where the arrow hits the tree.

How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Find td.

Any suggestions? Thanks for any reply
Click to expand...

u need the initial velocity of the arrow to do this, don;t u ?
 
Originally posted by: StevenYoo
Originally posted by: agahnim
I'm having trouble solving this problem.

An arrow is shot at an angle of 45 degrees above the horizontal. The arrow hits a tree a horizontal distance of D = 220 meters away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity g = 9.8.

Find ta, the time that the arrow spends in the air.

Suppose someone drops an apple from a vertical distance of 6.0 meters , directly above the point where the arrow hits the tree.

How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Find td.

Any suggestions? Thanks for any reply
Click to expand...

u need the initial velocity of the arrow to do this, don;t u ?
Click to expand...


No, because you already have the distance and the location of where it hit. Any more velocity and it would have went farther, any less and it would have fell shorter.
 
Dont think its that detailed this is Physics 1 for Engineers. I got some help from a tutor and got some equations like these a=g, Vi = Vy, Vy = Sin 45, and Vx = V cos 45 = 220/t but not really sure what to do with them.
 
Originally posted by: agahnim
Dont think its that detailed this is Physics 1 for Engineers. I got some help from a tutor and got some equations like these a=g, Vi = Vy, Vy = Sin 45, and Vx = V cos 45 = 220/t but not really sure what to do with them.
Click to expand...

All you have to do it break it down into the horizontal and vertical components. Law of compound motion.
 
Originally posted by: agahnim
Dont think its that detailed this is Physics 1 for Engineers. I got some help from a tutor and got some equations like these a=g, Vi = Vy, Vy = Sin 45, and Vx = V cos 45 = 220/t but not really sure what to do with them.
Click to expand...

the Vx and Vy represent the horiz and vert components of the initial velocity, respectively.

looking at the horiz:

D(horiz) = 220 = (Vx)(ta) = (Vcos45)(ta) = 0.707V(ta)

and vert:

vf = vi + at

since Vf = 0 at the top of any vertical flight,

0 = Vy + g(ta)

so that means:

ta = -(.707V)/9.8

*edit* crap why am i doing ur HW for u, haha
 
Originally posted by: StevenYoo
Originally posted by: agahnim
I'm having trouble solving this problem.

An arrow is shot at an angle of 45 degrees above the horizontal. The arrow hits a tree a horizontal distance of D = 220 meters away, at the same height above the ground as it was shot. Use for the magnitude of the acceleration due to gravity g = 9.8.

Find ta, the time that the arrow spends in the air.

Suppose someone drops an apple from a vertical distance of 6.0 meters , directly above the point where the arrow hits the tree.

How long after the arrow was shot should the apple be dropped, in order for the arrow to pierce the apple as the arrow hits the tree? Find td.

Any suggestions? Thanks for any reply
Click to expand...

u need the initial velocity of the arrow to do this, don;t u ?
Click to expand...

Not to mention that you need to have some knowledge about the aerodynamic properties for the arrow (Fletchings, Head type, shaft material: carbon fibre, Al, Wood,) etc all of these Have affect the way it shoots. I also need to add that Mass is an important factor as well.
 
The arrow will spend 6.7 seconds in the air.

Launch velocity will be 46.43 meters/second.

Peak height will be 55 meters.
 
Originally posted by: 91TTZ
The arrow will spend 6.7 seconds in the air.
Click to expand...

assuming it's an elven longbow fired by a lvl 4 ranger

*EDIT* i forgot, who happens to be spherical (for mathematical purposes)
 
Originally posted by: Googer
Not to mention that you need to have some knowledge about the aerodynamic properties for the arrow (Fletchings, Head type, shaft material: carbon fibre, Al, Wood,) etc all of these Have affect the way it shoots. I also need to add that Mass is an important factor as well.
Click to expand...

All you would realistically need is a ballistic coefficient (drag coefficient * reference area / mass). Because of the stability of the arrow, pitching moments (and mass distribution) and lifting forces would likely not be of concern. The actual material properties of the shaft are also probably negligible on the aerodynamic characteristics, as the different roughness values would probably have a very small effect on the boundary layer at these scales.

The fletchings are the biggest concern. Because of the severe aeroelastic effects these can not be effectively computationally modeled with any accuracy. I will go ahead and order a wind tunnel test in the 3'x3' ATOT subsonic wind tunnel facility as soon as possible. There will be difficulty in measuring the drag forces on this object, but I feel that a lower mounted sting connected mid-shaft would best measure the forces with minimal interference. We should also try a range of Reynolds number to at least get a feel for scaling effects if we cannot realize the full flight velocity of the arrow in the wind tunnel.

Once the drag coefficient is determined I will promptly use a standard numerical ODE solver to find the flight time for the arrow.
 
Man...I thought this was going to be real physics question...like, "can somone explain the BCS theory of superconductivity" or something...

Oh well...🙁
 
Originally posted by: StevenYoo
Originally posted by: 91TTZ
The arrow will spend 6.7 seconds in the air.
Click to expand...

assuming it's an elven longbow fired by a lvl 4 ranger

*EDIT* i forgot, who happens to be spherical (for mathematical purposes)
Click to expand...


For these dumb math problems, they seem to want people to get the exact answers while conveniently ignoring details such as the Earth being round, there being air, objects having lift, etc.

They probably want a pure physics answer with vectors, velocities and accelerations without any other variables. Sort of like spaceflight.
 
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