To solve this problem, we can use trigonometry to find the distance the supplies travel and then use the formula distance = rate * time to find how long it takes for the supplies to move to the second floor.
First, let's find the distance the supplies travel:
We can see that the angle formed by the conveyor belt with the ground is 60°, which means the conveyor belt creates a right triangle with the ground. The vertical distance the supplies travel is 24 feet (height of the second floor). We can use trigonometry to find the hypotenuse (distance traveled by the supplies):
cos(60°) = adjacent/hypotenuse
cos(60°) = 24/hypotenuse
hypotenuse = 24 / cos(60°)
hypotenuse ≈ 48 feet
So, the supplies travel approximately 48 feet from one end of the conveyor belt to the other.
Now, let's find how long it takes for the supplies to move to the second floor:
We know that the belt moves at 75 ft./min., and the supplies need to travel 48 feet. Therefore, we can use the formula distance = rate * time to find the time it takes for the supplies to move to the second floor:
48 = 75 * time
time = 48 / 75
time = 0.64 minutes
Therefore, it takes approximately 0.6 minutes (or 0.6 * 60 = 36 seconds) for the supplies to move to the second floor.
The closest answer choice is:
42 ft.; 35.0 min.
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. 28 ft.; 0.4 min.
1 answer