Question

A conveyor belt is used to move sand from one place to another in a factory. The conveyor is tilted at an angle of 18° above the horizontal and 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. Determine the horizontal distance between the end of the conveyor belt and the middle of the collecting drum.

Answer 1

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

$y = yo+ V_y t +\frac{1}{2}gt^2$

$0 = 5 + 2sin18+ \frac{1}{2}*9.8t^2$

solving for t

t = 1.075 sec

for horizontal motion

$x = V_x t$

x = 2cos18*1.075

x = 2.044 m