Arrow's initial velocity (Force problem)


by thatgirlyouknow
Tags: arrow, force, initial, velocity
thatgirlyouknow
thatgirlyouknow is offline
#1
Sep8-07, 09:40 PM
P: 58
1. The problem statement, all variables and given/known data

An arrow, starting from rest, leaves the bow with a speed of 27.5 m/s. If the average force exerted on the arrow by the bow was increased 3 times and the arrow was accelerated over the same distance, then with what speed would the arrow leave the bow?

2. Relevant equations

F = ma, obviously. So if 3F = 3ma, then the acceleration would triple, because the mass of the arrow remains the same.

Vx=V0+at

3. The attempt at a solution

3*27.5 is wrong, so tripling the force doesn't automatically triple the initial velocity. I don't feel like I have enough information to work this problem, honestly.

Does anyone have any suggestions or help to offer?
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
learningphysics
learningphysics is offline
#2
Sep8-07, 09:55 PM
HW Helper
P: 4,125
You're right that acceleration triples. But you don't know the time... you know the distance is the same in both situations.

There's another kinematics equation that's useful in this circumstance. hint: it doesn't have time in it.
thatgirlyouknow
thatgirlyouknow is offline
#3
Sep9-07, 12:46 PM
P: 58
So using v^2 = v0^2 + 2ax, should I find the final velocity the first time? Using that the acceleration triples could give:

v^2 = v0^2 + 6ax

And the first launch is v^2 = 27.5^2 + 2ax. The distance is the same, so if one solves for x and sets the equations equal you get:

(v^2-v0^2)/6a =( v^2-(27.5^2))/2a

But that's still too many variables to solve! How am I supposed to know the final velocity and/or acceleration?

learningphysics
learningphysics is offline
#4
Sep9-07, 01:02 PM
HW Helper
P: 4,125

Arrow's initial velocity (Force problem)


In the first situation 27.5 is the final velocity. v0 = 0.
In the second situation, you're trying to calculate final velocity, and v0 = 0.

Write the two kinematics equations for the two situations... then try to see if you can eliminate a and x.

we're looking over the period in which the bow is accelerated... so the velocity with which the bow leaves, is the final velocity (at the end of the acceleration)
thatgirlyouknow
thatgirlyouknow is offline
#5
Sep9-07, 02:18 PM
P: 58
Well x is easily eliminated since it is the same in both equations. Solving for x and then setting the two equal to each other gives:

27.5^2/(2a) = v^2/(6a)

Rearranging and solving for v^2 gives:

2268.75a = v^2

But I'm still stuck with a, and have no idea where it could go or how to get rid of it.
learningphysics
learningphysics is offline
#6
Sep9-07, 02:23 PM
HW Helper
P: 4,125
Quote Quote by thatgirlyouknow View Post
Well x is easily eliminated since it is the same in both equations. Solving for x and then setting the two equal to each other gives:

27.5^2/(2a) = v^2/(6a)
Yes, exactly.

Rearranging and solving for v^2 gives:

2268.75a = v^2
No, you made a mistake in your algebra. You're almost there...
thatgirlyouknow
thatgirlyouknow is offline
#7
Sep9-07, 02:26 PM
P: 58
Oops, the a's cancel. My mistake.

So v = 47.63 m/s. Thank you so much! Problem solved. :D
learningphysics
learningphysics is offline
#8
Sep9-07, 02:26 PM
HW Helper
P: 4,125
Quote Quote by thatgirlyouknow View Post
Oops, the a's cancel. My mistake.

So v = 47.63 m/s. Thank you so much! Problem solved. :D
yup. that's the answer.

no prob. you're welcome.
hitman38
hitman38 is offline
#9
Aug25-09, 09:57 PM
P: 3
I have different question;
What distance an arrow travel if I throw the arrow with 200N force and 20 degrees?
The mass of the arrow is 100 gr.
Please help,Thanks


Register to reply

Related Discussions
Simple Initial Velocity Problem Introductory Physics Homework 1
initial velocity Introductory Physics Homework 0
Given an initial position and velocity of a receiver, find the velocity of a ball Introductory Physics Homework 7
initial velocity Introductory Physics Homework 4
Initial velocity Introductory Physics Homework 5