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# Physics/Speed & Weight of the Arrow

Question
Dear Steve, good morning to you.

I have a question to solve that it is:
"If I have an arrow with weight in 425 grams and this arrow it is
launched by a strong bow at a long distance, creating a parabola and when this arrow reaches the curve of the parabola (tangent), beginning dropping at height of about 30 meter, which will be the speed and a relative weight when the arrow touch the ground?"
I think that I put all information necessary to you analyze this question.
Sincerely,
Ary Neiva

Hello Ary,

I can help you determine the vertical component of the velocity at touchdown, but I don't know the horizontal details. Therefore I can't determine the horizontal component of the velocity, or the resultant velocity.

Use the kinematic formula
Vf^2 = Vi^2 + 2*a*h
where Vi = 0 -- the conditions at the peak of the trajectory are taken as the initial conditions,
a = g = 9.8 m/s^2,
h = 30 m. Vf is the vertical component of the velocity immediately before it reaches the ground. If the arrow had been shot straight up, this would be the velocity it hit the ground with.

I'm not familiar with the phrase "relative weight" in a physics sense. If it had been shot straight up, the velocity immediately before it reaches the ground would be Vf from above. And the momentum = m*Vf. The ground would give it an impulse equal to F*t which is also equal to the change in momentum. Since the arrow comes to a stop, the change in momentum is m*Vf. Then we could write
F*t = m*Vf
Now, if we only knew how quickly it comes to a stop, perhaps 0.01 s or perhaps 0.05 s, we could solve the above equation for F and know the force exerted to stop it. If it had been shot straight up. That force is the what I might guess as the meaning of relative weight.

I hope this helps,
Steve
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Steve good morning to you. I had formulated my question with some mistakes. For example, the weight of the arrow it’s not measure in Grams, but in GRAINS!! And with this error I can imagine your difficulty to understand my question. And the worst one was the value referred about the weight of the arrow, when I wrote “425 grams”, inacceptable value!!!! Imagine the guy with a arrow measuring almost 1 pound!!! :) Even so, you gave me your response, for which I say to you my thanks so much. You really are a good guy!!! Again thanks, and sorry about my mistakes. Now I am learning about Archery and trying to understand the right words and measures that are used in this sport. When I will have more skills for understand about Archery, I will send you my question better formulated. Best regards, Ary Neiva

Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University