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