Question

A conveyor belt carries supplies from the first floor to the second floor, which is 30 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? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?

A. 52 ft; 42 min

B. 42 ft; 26.3 min

C. 17 ft; 1.1 min

D. 35 ft; 0.5 min

Answer 1

The supplies travel a distance of 15 feet from one end of the conveyor belt to the other. It takes the supplies 0.2 minutes to move to the second floor.

Step-by-step explanation:

To find the distance the supplies travel from one end of the conveyor belt to the other, we can use trigonometry. The 60° angle forms a right triangle with the horizontal distance traveled by the supplies as the adjacent side and the vertical distance as the opposite side. We can use the cosine function to find the horizontal distance:

Adjacent = Hypotenuse * Cos(60°)

Since the hypotenuse is the distance the supplies travel, we can plug in the given value of 30 feet:

Adjacent = 30 ft * Cos(60°) = 15 ft

Therefore, the supplies travel a distance of 15 feet from one end of the conveyor belt to the other.

To find the time it takes for the supplies to reach the second floor, we can use the formula:

Time = Distance / Speed

Since we found the distance to be 15 feet, we can plug in the given speed of 75 ft/min:

Time = 15 ft / 75 ft/min = 0.2 min

Rounded to the nearest tenth of a minute, it takes the supplies 0.2 minutes to move to the second floor.