Question

1) Assume that a series of experiments are correctly designed and performed. How many are needed to disprove a theory? How many are needed to prove a theory? (2) Given the vectors: a = 4 i - 3 j and b = 6 i + 8 j Find the magnitude and direction of: a, b, a + b and a - b (3) A vector has a magnitude of 7.3 units and a direction of 250 degrees (measured counterclockwise from the positive x-axis). Find its x- and y-coordinates and write the vector in terms of the unit vectors i and j. (4) The speed of light is 300, 000 km/s. The Astronomical Unit or distance from the Earth to the Sun is 150,000,000 km. The length of a light year can be found in Appendix E. Express the speed of light in units of: a. AU per minute b. light years per year

Answer 1

1) there should be two to disprove it and one to prove it

2) a = 4i - 3j

b = 6i + 8j

a+ b = (4i -3j) + (6i + 8j)

= 10i + 5j

direction = tan^-1 ( 5/10) = 26.56^o ( from x-axis in counter clockwise direction)

a-b = (4i - 3j) - (6i + 8j)

= -2i -11j

angle = 180 + tan^-1(-11/-2) = 259.7^o from x-axis in counter clockwise direction

3) x-component = -7.3 cos (270 -250) = -6.86

y-component = 7.3 sin (270-250) = 2.5

Vector = -6.86i + 2.5j