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
I think it's...
B. 35 ft.; 0.4 min.
Hope this helps.
Well, here's a fun fact for you: conveyor belts can sometimes have a mind of their own! But fear not, I'm here to help you solve this problem with a touch of humor.
To find the distance the supplies travel from one end of the conveyor belt to the other, we can use a bit of trigonometry. Since the belt makes a 60-degree angle with the ground, we can imagine a right-angled triangle.
The side opposite the 60-degree angle represents the vertical distance the supplies travel (30ft), and the hypotenuse of the triangle represents the total distance traveled. We can use the sine function to solve for the hypotenuse:
sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 30ft/hypotenuse
To find the hypotenuse, we can rearrange the equation:
hypotenuse = 30ft / sin(60 degrees)
Using a bit of math magic, we find that the hypotenuse is approximately 34.64ft. Rounding it to the nearest foot, the supplies travel about 35ft from one end of the conveyor belt to the other.
Now, for the time it takes for the supplies to reach the second floor. We know that the belt moves at a speed of 80ft/min and the supplies have to travel 35ft.
To find the time, we can use the simple formula:
time = distance / speed
Plugging in the values, we get:
time = 35ft / 80ft/min
Calculating it, the supplies take roughly 0.44 minutes. Rounding it to the nearest tenth of a minute, it takes about 0.4 minutes for the supplies to move to the second floor.
So, the correct answer would be:
35 ft; 0.4 min
Now that we've solved this, let's hope the supplies aren't playing any tricks on the conveyor belt! Happy math-ing!
To find the distance the supplies travel from one end of the conveyor belt to the other, we can use trigonometry. The supplies move along the conveyor belt, which makes a 60 degree angle with the ground. We can use the sine function to find the length traveled.
The formula is: opposite/hypotenuse = sin(angle)
The opposite side is the vertical displacement, which is 30ft.
The hypotenuse is the distance traveled by the supplies on the conveyor belt.
By rearranging the formula, we get: hypotenuse = opposite / sin(angle)
Plugging in the values: hypotenuse = 30ft / sin(60°) ≈ 34.64ft
Therefore, the supplies travel approximately 34.64ft from one end of the conveyor belt to the other.
To find the time it takes for the supplies to move to the second floor, we can use the formula:
time = distance / speed
Plugging in the values: time = 34.64ft / 80ft/min ≈ 0.433 min ≈ 0.4 min (rounded to the nearest tenth of a minute)
So, the correct answer is:
35 ft; 0.4 min
To solve this problem, we can use trigonometry. Let's start by finding the horizontal distance traveled by the supplies from one end of the conveyor belt to the other.
We know that the angle between the ground and the conveyor belt is 60 degrees. This forms a right triangle, where the hypotenuse represents the conveyor belt, the vertical leg represents the height difference between the two floors (30ft), and the horizontal leg represents the distance traveled by the supplies.
Using trigonometry, we can determine the horizontal distance (x) using the formula:
cos(60°) = adjacent/hypotenuse
cos(60°) = x/30
To find cos(60°), we can refer to a reference table or use a calculator. The cosine of 60 degrees is 0.5.
0.5 = x/30
Cross-multiplying:
0.5 * 30 = x
x = 15ft
So, the supplies travel a horizontal distance of 15 feet from one end of the conveyor belt to the other.
Now, let's calculate the time it takes for the supplies to move from the first floor to the second floor.
We know that the belt moves at a speed of 80ft/min. Since the supplies travel a vertical distance of 30ft, we can use the formula:
time = distance/speed
time = 30ft/80ft/min
Simplifying:
time = 0.375 min
Rounding to the nearest tenth:
time ≈ 0.4 min
Therefore, the supplies take approximately 0.4 minutes (or 0.4 minutes) to move from the first floor to the second floor.
So, the answer is option B: 35ft; 0.4 min.
Make a sketch.
using trig: sin60 = 30/h ----> h = 30/sin60 = appr 34.64
to go 34.64 ft at 80 ft/min would take
34.64/80 or .43 minutes