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A dart gun is fired while being held horizontally at a height of 0.85 m above ground level, and at rest relative to the ground. Thedart from the gun travels a horizontal distance of 4.27 m. A child holds the same gun in a horizontal position while sliding down a42.8◦ incline at a constant speed of 3.09 m/s. What horizontal distance x will the darttravel if the child fires the gun forward whenit is 0.819 m above the ground? The acceleration due to gravity is 9.8m/s2

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First the dart gun is fired horizontally at rest, at a height H1 =0.85 m above the ground. The trajectory of the dart is half of a parabola.

On the y axis the motion is free fall.

`H1 = (g*(t1)^2)/2` , hence `t1 =sqrt((2*H1)/g) =sqrt(2*0.85/9.81) =0.1733 s`

On the x axis the motion is uniform

`X1 = V_(1x)*t` , hence `V_(1x) =(X1)/t...

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