To find the distance the supplies travel along the conveyor belt, we need to use trigonometry. Since the belt makes a 60° angle with the ground, we can use the cosine function to find this distance:
cos(60°) = adjacent/hypotenuse
cos(60°) = x/24
x = 24*cos(60°)
x = 24*0.5
x = 12 ft
So, the supplies travel 12 feet from end to end along the conveyor belt.
To find how long it takes the supplies to move to the second floor, we can use the Pythagorean theorem. The distance up the second floor is the opposite side of a right triangle with a hypotenuse of 12 ft and an angle of 60 degrees. We can find the height using the sine function:
sin(60°) = opposite/hypotenuse
sin(60°) = x/12
x = 12*sin(60°)
x = 12*√3/2
x = 6√3 ft
Now, we can find the time it takes for the supplies to reach the second floor by dividing the height by the speed of the belt:
Time = 6√3 ft / 75 ft/min
Time = 0.4 minutes
Therefore, the supplies travel 12 feet from end to end along the conveyor belt and it takes 0.4 minutes for the supplies to move to the second floor. The closest answer choice is:
28 ft.; 0.4 min.
A conveyor belt carries supplies from the first floor to the second floor, which is 24 feet higher. The belt makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other to the nearest foot? If the belt moves at 75 ft./min., how long does it take the supplies to move to the second floor to the nearest tenth of a minute?
(1 point)
Responses
34 ft.; 21.0 min.
34 ft.; 21.0 min.
42 ft.; 35.0 min.
42 ft.; 35.0 min.
14 ft.; 1.0 min.
14 ft.; 1.0 min.
28 ft.; 0.4 min.
1 answer