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Topic 1.1 Extended Problem solving strategies

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Topic 1.1 ExtendedProblem solving strategies

Topic 1.1 ExtendedA - Problem solving strategies

One of the main “headaches” of physics has traditionally been the problem solving aspect of it.

Generally, a problem will be posed by someone else, and YOU will have to find the solution.

Oftentimes at first glance, it will seem that there is not enough information. Or the problem may just seem impossible.

A possible problem-solving strategy will be illustrated on the next slide. But the more practice you get, the easier problem solving will become. Don’t lose faith!

5 km/h

5 km/h

FYI: A little thought may convince you that he reverses direction an infinite number of times. Thus he has traveled an infinite sum of progressively shrinking distances.

FYI: A little thought may convince you that he reverses direction an infinite number of times. Thus he has traveled an infinite sum of progressively shrinking distances.

Topic 1.1 Extended A - Problem solving strategies

FYI: Our first “attack” might be a frontal assault, wherein we find a pattern for these distances, and sum them up. It can be done!

Consider two trains approaching each other on the same track. When they are 10 km apart a fly, who can travel at 2 m/s leaves one train and flies to the other, continuing to go back and forth without resting until the trains collide. How far, in total, does the fly travel?

FYI: But an easier way is to use our d = rt formula:

10 km

5 km/h

5 km/h

Topic 1.1 Extended A - Problem solving strategies

10 km

Consider two trains approaching each other on the same track. When they are 10 km apart a fly, who can travel at 2 m/s leaves one train and flies to the other, continuing to go back and forth without resting until the trains collide. How far, in total, does the fly travel?

Since the trains are each moving at 5 km/h, they approach each other at 10 km/h.

Since they are 10 km apart when the fly begins, he has exactly 1 hour to fly.

That is to say, he has 60 minutes, or 3600 seconds to fly.

Since he is flying at 2 m/s, we can use the formula d = rt to get the total distance of 7200 m, or 7.2 km.

Do the TRANSLATION

5 km/h

Do the PHYSICS

Do the MATH

Do the CHECK

FYI: Sometimes a check can’t be done – after all, what is reasonable here? But usually, an estimate can convince you that your answer is in the ball park.

FYI: We used unit conversions after our translation, demonstrating that the particular order shown is NOT the only order. BE FLEXIBLE, and develop your own strategy.

Topic 1.1 Extended A - Problem solving strategies

Here is a possible problem solving strategy:

Draw a picture

List and label

The trains, the arrows and the labels all fit in this category.

Do unit conversions

Determine attack angle

Determine relevant equations

Use d = rt.

Don’t try infinite sum.

Manipulate equations

Substitute and solve.

No manipulation of equation is needed, since we are looking for d.

Do calculations

Check reasonableness

Does the answer seem reasonable?

Topic 1.1 Extended A - Problem solving strategies

What is the area of a circle in m2 if it has a diameter of 1.25 cm?

Do calculations

Determine attack angle

Draw a picture

R = D ÷ 2

Find R then use the area formula.

R = 0.0125÷ 2

R = 0.00625 m

Determine relevant equations

A = πR2

D = 1.25 cm

A = π·0.006252

List and label

D = 2R

A = 0.000122718

A = πR2

A = 0.000123 m2

Do unit conversions

Check reasonableness

Manipulate equations

1 m

100 cm

D = 1.25 cm

·

R = D ÷ 2

Actual size

D = 0.0125 m