The distance that the supplies travel can be calculated using trigonometry. Since the angle of elevation is 60°, we can use the sine function to find the hypotenuse:
sin(60°) = opposite / hypotenuse
sin(60°) = 12 / hypotenuse
hypotenuse = 12 / sin(60°)
hypotenuse ≈ 13.9 ft
Therefore, the distance the supplies travel from one end of the conveyor belt to the other is approximately 13.9 ft.
To find the time it takes for the supplies to move to the second floor, we need to find the horizontal component of the distance, which is given by:
cos(60°) = adjacent / hypotenuse
cos(60°) = horizontal distance / 13.9
horizontal distance = 13.9 * cos(60°)
horizontal distance ≈ 6.95 ft
Now, we can find the time it takes for the supplies to move using the horizontal distance and the speed of the belt:
Time = distance / speed
Time = 6.95 ft / 80 ft/min
Time ≈ 0.087 min
Therefore, the supplies take approximately 0.1 minute to move from the first floor to the second floor. Since none of the provided options match exactly, the closest one would be:
A. 17 ft ; 0.2 min
A conveyor belt carries supplies from the first floor to the second floor, which is 12 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? If the belt moves at 80 ft / min how long does it take the supplies to move to the second floor to the nearest tenth of a minute.
A. 17 ft ; 0.2 min
B. 35 ft ; 0.4 min
C. 42 ft ; 0.5 min
D. 52 ft 0.6 min
1 answer