A conveyor belt carries supplies from the first floor to the second floor which is 30ft higher. The belt makes a 60 degree 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 80ft/min how long does it take the supplies to move to the second floor to the nearest tenth of a minute
17ft; 0.2 min
35 ft; 0.4 min
42ft; 0.5 min
52ft; 0.6 min
To find the distance traveled by the supplies from one end of the conveyor belt to the other, we can use trigonometry.
The vertical displacement (height) is given as 30ft, and the angle with the ground is 60 degrees. We can use the sine function, which relates the opposite side (vertical displacement) to the hypotenuse (distance traveled by supplies).
sin(angle) = opposite / hypotenuse
sin(60) = 30 / hypotenuse
hypotenuse = 30 / sin(60)
hypotenuse ≈ 34.64 ft
So, the supplies travel approximately 34.64 ft from one end of the conveyor belt to the other.
To find the time it takes for the supplies to move from the first floor to the second floor, we can use the formula: time = distance / speed.
The speed of the belt is given as 80 ft/min.
time = 30 ft / 80 ft/min
time ≈ 0.375 min
Rounding to the nearest tenth of a minute, we get approximately 0.4 min.
Therefore, the correct answer is:
35 ft; 0.4 min.
To determine the distance the supplies travel from one end of the conveyor belt to the other, we can use trigonometry. Given that the belt makes a 60 degree angle with the ground and moves 30ft vertically, we can calculate the distance traveled by using the sine function.
The sine function relates the length of the side opposite an angle to the hypotenuse of a right triangle. In this case, the length of the side opposite the angle (vertical distance) is 30ft, and the hypotenuse (distance traveled) is what we want to find.
Using the formula sin(angle) = opposite / hypotenuse, we can rearrange the formula to solve for the hypotenuse:
hypotenuse = opposite / sin(angle)
hypotenuse = 30ft / sin(60 degrees)
hypotenuse = 30ft / 0.866
Calculating this, we find that the hypotenuse (distance traveled by the supplies) is approximately 34.64 ft. Since we are asked for the answer to the nearest foot, the supplies travel approximately 35ft from one end of the conveyor belt to the other.
To calculate the time it takes for the supplies to move from the first floor to the second floor, we can use the formula: time = distance / speed.
Given that the belt moves at 80 ft/min and the distance traveled is 35 ft, we can calculate the time as follows:
time = 35ft / 80 ft/min
time ≈ 0.4375 min
Rounding this value to the nearest tenth, we find that it takes approximately 0.4 minutes for the supplies to move from the first floor to the second floor.
Therefore, the correct answer is:
35 ft; 0.4 min
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