Respuesta :
Answer:
x = 2.044 m
Explanation:
given data
initial vertical component of velocity = Vy = 2sin18
initial horizontal component of velocity = Vx = 2cos18
distance from the ground yo = 5m
ground distance y = 0
from equation of motion
[tex]y = yo+ V_y t +\frac{1}{2}gt^2[/tex]
[tex]0 = 5 + 2sin18+ \frac{1}{2}*9.8t^2[/tex]
solving for t
t = 1.075 sec
for horizontal motion
[tex]x = V_x t[/tex]
x = 2cos18*1.075
x = 2.044 m
The motion of sand is due to the movement of conveyor belt. The horizontal distance between the end of the conveyor belt and the middle of the collecting drum is 2.044 meters.
What is equation of motion?
The equation of motion is the relation between the distance, velocity, acceleration and time of a moving body.
The second equation of the motion for distance can be given as,
[tex]y=ut+\dfrac{2}{2}gt^2[/tex]
Here, [tex]u[/tex] is the initial body, [tex]g[/tex] is the acceleration of the body due to gravity and [tex]t[/tex] is the time taken by it.
Given information-
The conveyor is tilted at an angle of 18° above the horizontal.
The Sand is moved without slipping at the rate of 2 m/s.
The sand is collected in a big drum 5 m below the end of the conveyor belt.
The horizontal component of the velocity is given as,
[tex]v_y=2\cos 18[/tex]
The vertical component of the velocity is given as,
[tex]v_y=2\sin18[/tex]
Put the value in the above equation as,
[tex]y-y_0=v_yt+\dfrac{1}{2}gt^2[/tex]
[tex]0-5=2\sin18 (t)+\dfrac{1}{2}\times9.8\tiems t^2\\t=1.075\rm sec[/tex]
The horizontal distance between the end of the conveyor belt and the middle of the collecting drum is,
[tex]d=v_xt\\d=2\cos18\times1.075\\d=2.044\rm m[/tex]
Thus, the horizontal distance between the end of the conveyor belt and the middle of the collecting drum is 2.044 meters.
Learn more about the equation of motion here;
https://brainly.com/question/13763238
