Diagram Blitz 2

GES 131

Draw Five Diagrams on Two Minutes Each

Directions

Each slide will have a problem.

You have 2 minutes to draw and label a diagram or diagrams that “tell the story” in a precise mathematical way.

Do not solve the problems. After 2 minutes the slide will change.

Problem 1A heavy safe is placed on top of two cylindrical

bars with diameter 4” each in order to move it.

If there is no slipping, and the bars roll so each has rotated 10 degrees, how far has the safe moved?

Problem 2We start with a box whose bottom is 12” by 12”.

The largest possible round can of paint is placed in the box.

The four largest possible round cans of paint are then placed in the box. Find the radius of one of these four cans of paint.

Problem 3The body of a two door sports car is 6” wide.

Each door is 3” long and opens a maximum of 50 degrees.

When both doors are fully open, what is the distance between the ends of the doors that are furthest away from the car.

Problem 4At Burgerworld, hamburger patties are placed on

a conveyer belt at one side of the oven, move along a conveyer belt at 1.5” per second while they cook, then exit fully cooked on the other side.

The oven is 60” wide.

A patty starts into the oven at time t=0.

Find the percentage the patty is cooked as a function of time.

Problem 5Rachel can get from her home to class on time

if she drives 60 mph.

She drives a fraction 0 < p < 1 of the distance at speed r < 60, then realizes she has been driving too slow.

How fast must she drive to arrive on time?

Diagram Blitz 2

GES 131

Draw Five Diagrams on Two Minutes Each

Problem 1A heavy safe is placed on top of two cylindrical bars

with diameter 4” each in order to move it.

If there is no slipping, and the bars roll so each has rotated θ radians, how far has the safe moved?

θ

s

s

s

s

Problem 2We start with a box whose bottom is 12” by 12”.

The largest possible round can of paint is placed in the box.

The four largest possible round cans of paint are then placed in the box. Find the radius of one of these cans of paint.

r

6

6

rr

x

6

Problem 3The body of a two door sports car is 6’ wide.

Each door is 3’ long and opens a maximum of 50 degrees.

When both doors are fully open, what is the distance between the ends of the doors that are farthest away from the car.

50o

50o

3’

3’

6’d

h

h

Problem 4At Burgerworld, hamburger patties are placed on a

conveyer belt at one side of the oven, move along a conveyer belt at 1.5” per second while they cook, then exit fully cooked on the other side. The oven is 60” wide. A patty starts into the oven at time t=0. Find the percentage the patty is cooked as a function of time.

60”

1.5t

Problem 5Rachel can get from her home to class on time if she

drives 60 mph.

She drives a fraction 0 < p < 1 of the distance at speed r < 60, then realizes she has been driving too slow.

How fast must she drive to arrive on time?

D

pDat speed r

D - pDat speed v