How Fast Does an Arrow Travel When Shot Horizontally?

In summary, to calculate the initial velocity of an arrow launched horizontally, we can first find the time it takes for the arrow to reach the ground vertically using the equation y=.5(-9.8)t^2. Then, we can use this time to calculate the initial velocity using the equation Yf=Yo+Voy-.5gt^2, where Yf is the final vertical position, Yo is the initial vertical position, Voy is the initial vertical velocity, and g is the acceleration due to gravity. In this specific problem, the initial velocity of the arrow is 33 m divided by 0.553 seconds, which is approximately 59.7 m/s.
  • #1
runningirl
118
0
please help! projectile motion question

Homework Statement



You have a friend who is an archer and she wants to know how fast the arrows leave her bow. You have her launch an arrow horizontally, 1.5 m above the ground, and find that the arrow lands 33 m away. What is the initial velocity of the arrow as it leaves the bow?

Homework Equations



y=.5(-9.8)t^2

The Attempt at a Solution



i don't know where to start with this problem. I'm sorry :(
 
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  • #2


This is a two stage problem. You first have to find the time it takes the arrow to reach the ground vertically. Then you can use that time to calculate the inital velocity of the arrow horizontally.
 
  • #3


runningirl said:

Homework Statement



You have a friend who is an archer and she wants to know how fast the arrows leave her bow. You have her launch an arrow horizontally, 1.5 m above the ground, and find that the arrow lands 33 m away. What is the initial velocity of the arrow as it leaves the bow?

Homework Equations



y=.5(-9.8)t^2

The Attempt at a Solution



i don't know where to start with this problem. I'm sorry :(
Yf=Yo+Voy-.5gt^2
=1.5+0-4.9t^2
1.5/4.9=t^2
t=0.553 seconds
...
 

Related to How Fast Does an Arrow Travel When Shot Horizontally?

1. What is projectile motion?

Projectile motion is the movement of an object through the air or space with only the force of gravity acting upon it. It follows a curved path known as a parabola due to the combination of horizontal velocity and vertical acceleration.

2. How do you calculate the trajectory of a projectile?

The trajectory of a projectile can be calculated using the following equations:
Horizontal distance: d = v0 * cosθ * t
Vertical distance: h = v0 * sinθ * t - 1/2 * g * t2
Total distance: R = v0 * sin2θ / g

3. What are the factors that affect projectile motion?

The factors that affect projectile motion are the initial velocity, the angle of projection, the mass of the object, and the gravitational force. Other factors such as air resistance and wind can also have an impact on the trajectory of the projectile.

4. How does the height of the projectile affect its trajectory?

The height of the projectile affects its trajectory in terms of the time it takes to reach its highest point and the distance it travels horizontally. A higher initial height will result in a longer flight time and a longer horizontal distance, while a lower initial height will result in a shorter flight time and a shorter horizontal distance.

5. Can you calculate the maximum height and distance of a projectile?

Yes, the maximum height and distance of a projectile can be calculated using the equations:
Maximum height: hmax = v0 * sin2θ / 2g
Maximum distance: dmax = v0 * sin2θ / g

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