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

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To solve the problem of how far the dart will travel when fired from a moving incline, it's essential to calculate the initial velocity components of the dart based on the child's speed and the incline angle. The child's horizontal speed is determined by multiplying their speed down the incline by the cosine of the incline angle, while the vertical speed is found using the sine function. The dart's initial velocity combines these components, allowing for the calculation of the horizontal distance it will travel after being fired from a height of 1.5 m. Understanding projectile motion principles, including the effects of gravity on the vertical component, is crucial for determining the total distance traveled. This problem requires careful consideration of both the incline's angle and the initial conditions of the dart's launch.
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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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Add the childs x and y (horizontal and vertical) components of speed as intial velocity of the dart.
 

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