The Art of Estimating

1.

Estimate how many standard soccer balls it would take to fill the Hennings 201 auditorium.¹

2.

Estimate the number of sand (quartz) grains there are in 1 metric ton of moderately coarse sand.

3.

An open tank of water has a uniform horizontal cross section of 2.4 m². When initially filled to a depth of 2.7 m, it loses water through a leak in its base at a rate of 2.0 litres per hour. Assuming no evaporative losses and that the rate of flow through the leak is proportional to the depth of water in the tank, calculate or estimate the leakage rate (again in litres per hour) 10 days later. What fraction of the water initially in the tank will already have leaked out by that time?

4.

A steel ball (from a ball bearing) is dropped from the roof of a building with zero initial velocity. Disregard air friction.² An observer standing behind a 140 cm high window notes that the ball takes 0.125 s to fall past the window. The ball continues to fall until it hits the sidewalk below, where it makes a perfectly elastic collision³ and reappears at the bottom of the window 2.1 s after it passed that point on the way down. How tall is the building?

(Note: the ball should have the same speed going up as it did at the same position coming down, if the collision is truly perfectly elastic and there is no air friction.)

ASSIGNMENT FORMAT:

• Single sided.

• Write and draw clearly and æsthetically.

• For each problem, explain your reasoning with a few concise words.

• Every problem must be accompanied by a diagram.

• Draw a rectangular box around your .

• Leave adequate space; do not squeeze too much onto one page.