Answer:
angle at which the cutter should be set = 32°
Explanation:
We are given;
Speed of conveyor belt; v1 = 15 cm/s
Width;w = 72 cm
Speed of the cutter that moves across the width; v2 = 24 cm/s
Let's calculate time;
Since the width and the rate at which the cutter works per seconds is given, thus;
Time = w/v2
Time = 72/24 = 3 seconds
Now, we know that, velocity = distance/time
Thus, distance = velocity x time
So, distance covered;d = 15 x 3 = 45 cm
Now, for us to calculate the angle the cutter should be set, we would treat it as a triangle.
When the cutter cuts it, it covers a distance d which is perpendicular to the width.
Thus, to calculate the angle made with the width, we'll use trigonometric ratio.
Thus, d/w = tan θ where θ is the angle at which the cutter should be set.
So, 45/72 = tan θ
tan θ = 0.625
θ = tan^(-1)0.625
θ = 32°
