Respuesta :
Answer:
The distance between knothole and the paint ball is 0.483 m.
Explanation:
Given that,
Height = 4.0 m
Distance = 15 m
Speed = 50 m/s
The angle at which the forester aims his gun are,
[tex]\tan\theta=\dfrac{4}{15}[/tex]
[tex]\tan\theta=0.266[/tex]
[tex]\cos\theta=\dfrac{15}{\sqrt{15^2+4^2}}[/tex]
[tex]\cos\theta=0.966[/tex]
Using the equation of motion of the trajectory
The horizontal displacement of the paint ball is
[tex]x=(u\cos\theta)t[/tex]
[tex]t=\dfrac{x}{u\cos\theta}[/tex]
Using the equation of motion of the trajectory
The vertical displacement of the paint ball is
[tex]y=u\sin\theta(t)-\dfrac{1}{2}gt^2[/tex]
[tex]y=u\sin\theta(\dfrac{x}{u\cos\theta})-\dfrac{1}{2}g(\dfrac{x}{u\cos\theta})^2[/tex]
[tex]y=x\tan\theta-\dfrac{gx^3}{2u^2(\cos\theta)^2}[/tex]
Put the value into the formula
[tex]y=(15\times0.266)-(\dfrac{9.8\times(15)^2}{2\times(50)^2\times(0.966)^2})[/tex]
[tex]y=3.517\ m[/tex]
We need to calculate the distance between knothole and the paint ball
[tex]d=h-y[/tex]
[tex]d=4-3.517[/tex]
[tex]d=0.483\ m[/tex]
Hence, The distance between knothole and the paint ball is 0.483 m.
