Projectile Motion archers question

In summary, two archers shoot arrows with the same initial speeds and from the same place, but at different angles. One shoots at an angle of 45.0 degrees above the horizontal and lands 225m away, while the other shoots at 60.0 degrees. To find the distance between the two arrows when they land, we can use the formula R = \frac{u^2 \sin{(2\theta)}}{g} to calculate the ranges of both arrows and find the difference between them. This can be done by dividing the projectile motion into horizontal and vertical components and using the kinematic equations. Time is the same for both parts.
  • #1
ela88leo
1
0
Two archers shoot arrows in the same direction from the same place with the same initial speeds, but at different angles. One shoots at 45.0 degrees above the horizontal, while the other shoots at 60.0 degrees. If the arrow launched at 45.0 degrees lands 225m from the archer, how far apart are the two arrows when they land? assume that the arrows start at essentially ground level
 
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  • #2
My old teacher taught us a trick for projectile motions. Divide it into two parts: horizontal and verticle. The horizontal part would only have the equation v = d/t (since there is no acceleration in the horizontal component, and the verticle component would have the the regular kinematic equations.

Remember that time is the same for both parts.
 
  • #3
There is a very simple formula for calculating the range of a projectile in terms of the initial angle, starting speed and gravitational acceleration:

[tex]
R = \frac{u^2 \sin{(2\theta)}}{g}
[/tex]

compute the ranges of the two arrows and find out the difference in their ranges.
 

Related to Projectile Motion archers question

1. What is projectile motion?

Projectile motion refers to the motion of an object that is launched into the air and then moves along a curved path under the influence of gravity.

2. How does projectile motion apply to archery?

In archery, the arrow is the projectile and its motion is affected by the force of gravity, the initial velocity of the arrow, and any external factors such as wind resistance.

3. How is the trajectory of an arrow in projectile motion determined?

The trajectory of an arrow in projectile motion is determined by the initial velocity, angle of launch, and the force of gravity. These factors can be calculated using mathematical equations and can be affected by external factors like air resistance.

4. Can the trajectory of an arrow be altered in mid-flight?

Yes, the trajectory of an arrow can be altered in mid-flight through the archer's release, which can affect the initial velocity and angle of launch, and external factors such as wind resistance or obstacles in the arrow's path.

5. How can understanding projectile motion improve an archer's accuracy?

Understanding projectile motion can help archers make more accurate shots by allowing them to calculate the trajectory of their arrows and make adjustments for any external factors that may affect their shots. It can also help with determining the optimal angle of launch for a given distance.

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