# Finding How Far From the Ground an Object Hits Another

• Giygas72
In summary, the problem involves a knight's squire dropping a sandbag from a 12.0 metre tower while the knight shoots an arrow up at the sandbag from the base of the tower. The goal is to calculate the distance from the ground where the arrow strikes the sandbag and the arrow's initial velocity. The attempt at a solution involved using the equation vf^2 = vi^2 + 2g*t, but this was incorrect. The correct equation to use is d = vi*t + 1/2g * t^2, and the distance the sandbag falls in 1.1 seconds when dropped from rest should be used to solve the problem.
Giygas72

## Homework Statement

For archery practice, a knight's squire drops sandbags from a 12.0 metre tower. At exactly the same time the sandbag is dropped, the knight shoots an arrow up at the sandbag from the base of the tower. If the arrow strikes the sandbag at 1.1 seconds, calculate;

a) how far from the ground the arrow strikes the sandbag
b) the arrow's initial velocity

## Homework Equations

I chose vf^2 = vi^2 + 2g*t equation, ended up with this...

Other equations:
vf = vi + g*t
d = 1/2(vi + vf)*t
d = vi*t + 1/2g * t^2

## The Attempt at a Solution

= 0 + 2(-9.8)(12)
= (the square root of) 235.2
= 58m

Obviously incorrect. The biggest problem I'm having is finding the right equation to use. Where exactly do I go from here?

Giygas72 said:

## Homework Statement

For archery practice, a knight's squire drops sandbags from a 12.0 metre tower. At exactly the same time the sandbag is dropped, the knight shoots an arrow up at the sandbag from the base of the tower. If the arrow strikes the sandbag at 1.1 seconds, calculate;

a) how far from the ground the arrow strikes the sandbag
b) the arrow's initial velocity

## Homework Equations

I chose vf^2 = vi^2 + 2g*t equation, ended up with this...

Other equations:
vf = vi + g*t
d = 1/2(vi + vf)*t
d = vi*t + 1/2g * t^2

## The Attempt at a Solution

= 0 + 2(-9.8)(12) $\color{red} \Leftarrow$
= (the square root of) 235.2
= 58m

Obviously incorrect. The biggest problem I'm having is finding the right equation to use. Where exactly do I go from here?

What units are associated with the numbers on the line indicated with the arrow? What then should be the units of the result?

It would appear that you need to choose an equation that will give you the height of a sandbag at a given time t after it is dropped. Which of your Relevant Equations gives you distance with respect to time when acceleration is involved?

Giygas72 said:

## Homework Statement

For archery practice, a knight's squire drops sandbags from a 12.0 metre tower. At exactly the same time the sandbag is dropped, the knight shoots an arrow up at the sandbag from the base of the tower. If the arrow strikes the sandbag at 1.1 seconds, calculate;

a) how far from the ground the arrow strikes the sandbag
b) the arrow's initial velocity

## Homework Equations

I chose vf^2 = vi^2 + 2g*t equation, ended up with this...

Other equations:
vf = vi + g*t
d = 1/2(vi + vf)*t
d = vi*t + 1/2g * t^2

## The Attempt at a Solution

= 0 + 2(-9.8)(12)
= (the square root of) 235.2
= 58m

Obviously incorrect. The biggest problem I'm having is finding the right equation to use. Where exactly do I go from here?

There is no such kinematic equation as
vf^2 = vi^2 + 2g*t .​

There is one which states that vf2 = vi2 + 2g*d , but it's not much good for solving part a .

How far does any object fall in 1.1 seconds, when dropped from rest ?

## 1. How do you calculate the distance an object will travel before hitting the ground?

To calculate the distance an object will travel before hitting the ground, you will need to know the initial height of the object, the acceleration due to gravity, and the time it takes for the object to hit the ground. You can use the equation d = (1/2)gt^2, where d is the distance, g is the acceleration due to gravity (usually 9.8 m/s^2), and t is the time.

## 2. What factors affect the distance an object will travel before hitting the ground?

The distance an object will travel before hitting the ground is affected by the initial height of the object, the acceleration due to gravity, and the object's speed and direction of travel. Other factors that may affect the distance include air resistance, wind, and any obstacles in the object's path.

## 3. Can the distance an object travels before hitting the ground be calculated for any object?

Yes, the distance an object travels before hitting the ground can be calculated for any object as long as the necessary information is known. This includes the object's initial height, acceleration due to gravity, and the time it takes for the object to hit the ground.

## 4. How does air resistance affect the distance an object travels before hitting the ground?

Air resistance can decrease the distance an object travels before hitting the ground by slowing down the object's speed. This is because air resistance creates a force that opposes the object's motion, causing it to slow down and fall to the ground at a shorter distance.

## 5. Is there a way to accurately measure the distance an object travels before hitting the ground?

Yes, there are various methods for accurately measuring the distance an object travels before hitting the ground. These include using a measuring tape or ruler, using a motion sensor, or using a mathematical equation to calculate the distance. The accuracy of the measurement will depend on the precision of the measuring tool and the accuracy of the information used in the calculation.

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