How Far Will the Dart Travel When Fired from a Moving Incline?

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In summary, the conversation discusses using a dart gun and calculating the horizontal distance it will travel under different conditions. The first condition involves firing the gun while held horizontally at a certain height, while the second condition involves firing the gun while sliding down an incline at a constant speed. The question posed is how to calculate the horizontal distance the dart will travel when the gun is fired from a certain height. The solution involves adding the horizontal and vertical components of the child's sliding speed to the initial velocity of the dart.
  • #1
Nemi
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:cry: So many part to it its making me dizzy!

A dart gun is fired while being held horizontally at a height of 0.583 above ground level, and at rest relative to the ground. The dart from the gun travels a horizontal distance of 3.13 m. A child holds the same gun in a horizontal position while sliding down a 59.7 degree incline at a constant seed of 1.27m/s
What horizontal distance x will the dart travel if the child fires the gun forward when it is 1.5 m above ground?

:frown: Please help me understand what I need to do to solve this problem.
 
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  • #2
Add the childs x and y (horizontal and vertical) components of speed as intial velocity of the dart.
 
  • #3
I am feeling overwhelmed by the different parts and calculations involved. Thank you for any assistance you can provide.

I understand that this problem may seem daunting with multiple components and calculations involved, but let's break it down step by step.

First, we need to identify the given information. We know that the dart gun is initially at a height of 0.583 m and travels a horizontal distance of 3.13 m. We also know that the child is sliding down a 59.7 degree incline at a constant speed of 1.27 m/s. Finally, we need to find the horizontal distance x that the dart will travel when the child fires the gun at a height of 1.5 m.

To solve this, we can use the equations of projectile motion. The horizontal distance traveled by the dart can be calculated using the equation x = v0x * t, where v0x is the initial horizontal velocity and t is the time of flight. We can find v0x by using trigonometric functions to break down the initial velocity of the dart (which is the same as the child's sliding velocity) into its horizontal and vertical components. The vertical component will be affected by gravity, so we can use the equation y = y0 + v0yt - 1/2gt^2 to find the time of flight.

Once we have the time of flight, we can plug it into the first equation to find the horizontal distance x. Remember to take into account the initial horizontal distance of 3.13 m traveled by the dart before the child fires the gun.

I hope this helps guide you through the problem. Remember to take your time and break it down into smaller steps. Good luck!
 

FAQ: How Far Will the Dart Travel When Fired from a Moving Incline?

1. What is a projectile problem?

A projectile problem is a type of physics problem that involves calculating the motion of an object (the projectile) that is launched or thrown into the air and moves under the influence of gravity.

2. How do I solve a projectile problem?

To solve a projectile problem, you need to use the equations of motion and the principles of projectile motion. You will need to know the initial velocity of the object, the angle at which it was launched, and the acceleration due to gravity.

3. What information do I need to solve a projectile problem?

To solve a projectile problem, you will need to know the initial velocity of the object, the angle at which it was launched, and the acceleration due to gravity. You may also need to know the height of the object at certain points in its trajectory.

4. What are the key principles of projectile motion?

The key principles of projectile motion are that the horizontal and vertical components of the motion are independent of each other, the horizontal velocity remains constant, and the vertical velocity changes due to the influence of gravity. Additionally, the maximum height reached by the projectile is when the vertical velocity is zero.

5. Are there any common mistakes to avoid when solving a projectile problem?

Some common mistakes to avoid when solving a projectile problem include forgetting to convert units, using the wrong equations or values, and not considering the effects of air resistance. It is important to double-check all calculations and to carefully consider all relevant factors in the problem.

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