A dart gun is fired while being held hori- zontally at a height of 0.877 m above

Question

A dart gun is fired while being held hori-

zontally at a height of 0.877 m above ground

level, and at rest relative tothe ground. The

dart from the gun travels ahorizontal dis-

tance of 2.65 m. A child holds the samegun

in a horizontal position whilesliding down a

35.1? incline at a constantspeed of 1.01m/s.

The acceleration of gravity is9.8m/s2 .

35.1?

1.01 m/s

x

x

0.873 m

What horizontal distancex will thedart

travel if the child fires thegun forward when

it is 0.873 m above the ground? Answerin

units of m

Explanation / Answer

The dart gun is held horizontal at a height of 0.877m abovethe ground. The dart from the gun travels a horizontal distance of2.65 m. The incline is at an angle of = 35.1o abovethe horizontal position The speed of the child is u = 1.01 m/s The height of the dart gun is H = (u2 * sin2/2g)--------------(1) The range of the dart from the gun is R = (u2 * sin2/g) ---------------(2) Dividing equation (1) by equation (2),we get (H/R) = (u2 * sin2/2g) *(g/u2 * sin2) = (1/4)tan or tan = (4H/R) or = tan-1(4H/R) = tan-1(4 *0.873/2.65) = 52.93o Therefore,the horizontal distance x the dart will travel ifthe child fires the gun forward is x = (u2 * sin2/g) Here,u = 1.01 m/s and = 52.93o or x = ((1.01)2 * sin(2 *52.93o)/(9.8)) or x = 0.1001 m Therefore,the horizontal distance x the dart will travel ifthe child fires the gun forward is x = (u2 * sin2/g) Here,u = 1.01 m/s and = 52.93o or x = ((1.01)2 * sin(2 *52.93o)/(9.8)) or x = 0.1001 m

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