Calculating Projectile Motion: How Changing Force Affects Arrow Speed

In summary, the speed of an arrow leaving a bow is calculated using the equation v = sqrt(2Fd/mv). If the average force exerted on the arrow is doubled, the speed of the arrow would be 35.4 m/s, assuming all other variables remain the same. This is found by using the equation v = sqrt(4Fd/mv) and simplifying to v = sqrt(2) * 25. The concept of work done, or force multiplied by distance, is also mentioned in relation to the kinetic energy of the arrow.
  • #1
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An arrow, starting from rest, leaves the bow with a speed of 25.0 m/s . If the average force exerted on the arrow by the bow were double, all else remaining the same,with what speed would the arrow leave the bow
 
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  • #2
First case -

Fd = 1/2mv^2
v^2 = 2Fd/mv
v = sqrt(2Fd/mv)
25 = sqrt(2Fd/mv) - Equation (1)

Second case
(2F)d = 1/2mv^2
v^2 = 4Fd/mv
v = sqrt(4Fd/mv)
= sqrt(2)*sqrt(2Fd/mv)
= sqrt(2) * 25 (from (1))
v = 35.4 ms-1(3sf)

I think :D
 
  • #3
Fd = 1/2mv^2?
 
  • #4
isnt it d=1/2av^2
d=1/2(f/m)v^2
md=1/2(f)v^2?
 
  • #5
Hmm I am not familiar with those equations...

Work done is Force x Distance.

Since all the work goes into the kinetic energy of the arrow -

Work Done = Kinetic Energy
Fd = 1/2*mv^2

Yeah?
 
  • #6
hey, i never learned work done equations, we only used the big five kinematic equations
 

Related to Calculating Projectile Motion: How Changing Force Affects Arrow Speed

1. What is motion?

Motion refers to a change in an object's position or location with respect to time. It can be described using concepts such as speed, velocity, acceleration, and displacement.

2. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction of an object's motion. In other words, velocity takes into account the object's speed and the direction in which it is moving.

3. How is acceleration calculated?

Acceleration is the rate of change of an object's velocity. It can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (v2-v1)/t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time interval.

4. What is the difference between distance and displacement?

Distance is the total length of the path traveled by an object, while displacement is the distance between an object's starting and ending position. Displacement takes into account the direction of an object's motion, while distance does not.

5. What are some real-life examples of motion?

Some real-life examples of motion include a car moving down the street, a rollercoaster zooming down a track, a person walking across a room, and a ball rolling off a table. Essentially, any time an object changes its position or location, it is in motion.

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