Question

A dart gun is fired while being held horizontally at a height of 1.38m above ground level, and at rest relative to the ground. The dart from the fun travels a horizontal distance of 7.76. A child holds the same gun in a horizontal position while sliding down a 28.8 degrees incline at a constant speed of 1.78 m/s. (gravity is 9.8 m/ssquared)

What horizontal distance x will the dart travel if the child fires the gun forward when it is 0.561 m above the ground?

Answer 1

The first bits of information can be used to determine the muzzle velocity of the gun. Call that velocity Vm. Let T be the time it takes to hit the ground when fired horizontally.

7.76 m = Vm*T
(1/2)gT^2 = 1.38 m
T = 0.531 s
Vm = 14.6 m/s

When sliding down the 28.8 degree incline with the gun aimed horizontaly, the initial velocity components of the dart, in laboratory cordinates, are:
Vx = Vm + 1.78 cos28.9 = 16.2 m/s
Vy = -1.78 sin28.9 = -0.860 m/s
Y' (when fired) = 0.561 m
X' (when fired) = 0

Solve for X' when Y' = 0

You do the rest.