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

[Nemi]

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?

Please help me understand what I need to do to solve this problem.

 

[HallsofIvy]

Add the childs x and y (horizontal and vertical) components of speed as intial velocity of the dart.

 

[kyle8921]

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!