Question

21: pretend we are re - doing the falling bodies lab. this time, when we measure that at one click, the ball traveled exactly 1.25 meters. no range of error. at 2 clicks, we measure that the ball fell exactly 5 meters. again, no range of error. at 3 clicks, the ball has gone exactly 11.25 meters. once more, no error. we conduct the experiment 100 times and get exactly the same results every single time. there is no range of error in any of the results. in addition, we justify our method. if we were to collect these data, what would the results say about the platonic idea of never trusting the senses?
a) the platonic idea is reasonable, and scientists must always use pure logic;
b) the platonic idea is somewhat reasonable: in the 101st trial, the results may change dramatically;
c) the platonic idea is somewhat reasonable: in the 101st trial, the results may change slightly;
d) the platonic idea is somewhat unreasonable: in the 101st trial, the results may change slightly; trust that the idea may be philosophically relevant, but it may also stifle technological development: to trust that the results will be very similar on the 101st trial is reasonable.
22: in the falling bodies lab, we ______ the galilean idea that large things fall at the same speed as small things.
a) falsified
b) confirmed
c) neither confirmed nor falsified
d) both confirmed and falsified
23: according to the greek notion of how fast things fall, if something drops 4 feet in one unit time, how many feet will it drop in 4 units of time?
a) 4 feet; b) 8 feet; c) 12 feet; d) 16 feet; e) 20 feet.
24: according to galileos theory of how fast things fall, if something drops one foot in one unit time, how many feet will it drop in 4 units of time?
a) 4 feet; b) 8 feet; c) 12 feet; d) 16 feet; e) 20 feet.
25: when galileo dropped things off a high place, his efforts were:
a) largely ignored by all;
b) acclaimed by his university colleagues as a great advance in science;
c) denounced by his university colleagues; galileo was fired for violating greek philosophy.
d) denounced by pope urban vii.
e) answers c and d are both correct.
26: in the sequence 1, 4, 9, 16, 25, how does galileo get from 16 to 25?
a) squares 5
b) takes the square root of 5
c) adds 9 to 16
d) none of the above
27: what is the strongest degree of proof of a scientific hypothesis?
a) verification
b) falsification
c) failure by a single experiment to falsify
d) failure by numerous attempts to falsify.
onus: (2 points) pretend we are re - doing the falling bodies lab. we measure that at one click, the ball traveled exactly 1.25 meters. at 2 clicks, we measure that the ball fell exactly 5 meters. at 3 clicks, the ball has gone exactly 11.25 meters. we conduct the experiment 100 times and get exactly the same results every single time. if these are the data for the first 3 clicks, then how far will the ball fall at the 6th click? fill in the blank. show calculation

Explanation:

Step1: Analyze question 21

The Platonic idea of never trusting the senses is not fully applicable as in real - world experiments, while some consistency is observed, there is still a possibility of variation in results. So, it is somewhat unreasonable.

Step2: Analyze question 22

Galileo's idea that large and small things fall at the same speed has been confirmed through experiments like the Falling Bodies Lab.

Step3: Analyze question 23

According to the Greek notion of falling (assuming a linear relationship), if it drops 4 feet in 1 unit time, in 4 units of time it will drop 4×4 = 16 feet.

Step4: Analyze question 24

According to Galileo's theory of falling (distance \(d = \frac{1}{2}gt^{2}\), assuming initial velocity \(u = 0\), and in this simple case with a constant - acceleration model), if it drops 1 foot in 1 unit time, in 4 units of time \(d=\frac{1}{2}g(4)^{2}\). Since for 1 unit time \(d_1=\frac{1}{2}g(1)^{2}=1\) foot, for 4 units of time \(d = 16\) feet.

Step5: Analyze question 25

Galileo was denounced by Pope Urban VIII and his ideas were not well - received in some quarters due to conflict with traditional views.

Step6: Analyze question 26

In the sequence \(1,4,9,16,25\) which are \(1^2,2^2,3^2,4^2,5^2\), to get from \(16(4^2)\) to \(25(5^2)\), we add 9 (\(25-16 = 9\)).

Step7: Analyze question 27

The strongest degree of proof of a scientific hypothesis is the failure by numerous attempts to falsify it.

Step8: Analyze bonus question

Let's assume the relationship between the click number \(n\) and the distance \(d\) is a quadratic relationship \(d = an^{2}+bn + c\). Using the data points \((n = 1,d = 1.25)\), \((n = 2,d = 5)\) and \((n = 3,d = 11.25)\):

For \(n = 1\):

\(a\times1^{2}+b\times1 + c=1.25\), so \(a + b + c=1.25\)

For \(n = 2\):

\(a\times2^{2}+b\times2 + c=5\), so \(4a + 2b + c=5\)

For \(n = 3\):

\(a\times3^{2}+b\times3 + c=11.25\), so \(9a+3b + c=11.25\)
Subtract the first equation from the second: \((4a + 2b + c)-(a + b + c)=5 - 1.25\), \(3a + b=3.75\)
Subtract the second equation from the third: \((9a+3b + c)-(4a + 2b + c)=11.25 - 5\), \(5a + b=6.25\)
Subtract the new - obtained first equation from the second: \((5a + b)-(3a + b)=6.25 - 3.75\), \(2a=2.5\), \(a = 1.25\)
Substitute \(a = 1.25\) into \(3a + b=3.75\), \(3\times1.25 + b=3.75\), \(b = 0\)
Substitute \(a = 1.25\) and \(b = 0\) into \(a + b + c=1.25\), \(c = 0\)
So the formula is \(d = 1.25n^{2}\). When \(n = 6\), \(d=1.25\times6^{2}=1.25\times36 = 45\)

Answer:

1. d
2. b
3. d
4. d
5. e
6. c
7. d

Bonus: 45