Answer:
Explanation:
The angle of incidence and refraction are both measured from the normal
angle of incidence = 30°
angle of refraction = 23°
refractive index(n) = sini / sinr
n = sin30°/sin23°
n = 1.27965
refractive index (n) = 1/sinC
where C is the critical angle.
sinC= 1/n
C =arcsin (1/n)
C =arcsin (1/1.27965)
C = 51.39°
Answer:
(a) At what angle above the horizontal should the ball be thrown so that the runner will catch it just before it hits the ground? (b) How far does the woman run before she catches the ball?
(a) = 72.54°
≅ 72.5°
(b) = 33.4 m
Explanation:
see the attached file below
Answer:
A) Current equals the product of voltage and resistance for an ohmic device. False (current is voltage divided by resistance)
B) The greater the length of a wire, the higher the resistance of the wire. True (Resistivity is directly proportional to lenght and inversely proportional to the cross sectional area)
C) The potential difference produced by a battery varies depending on the circuit in which it is used. False (the potential difference of a battery is constant, the current drawn is what varies with circuit)
D) The thicker an electrical wire, the higher the resistance of the wire. False ( Resistivity is inversely proportional to the cross sectional area of the conductor).
Distribute the product:
a×b = (8i + j - 2k) × (5i - 3j + k)
a×b = 8i × (5i - 3j + k) + j × (5i - 3j + k) - 2k × (5i - 3j + k)
a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))
… … … + (5 (j×i) - 3 (j×j) + k×j)
… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))
Recall the definition of the cross product:
i×i = j×j = k×k = 0 (the zero vector)
i×j = k
j×k = i
k×i = j
and for any two vectors x and y, we have x×y = -(y×x).
So we have some cancellation and rewriting:
a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))
… … … + (5 (j×i) - 3 (j×j) + j×k)
… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))
a×b = (-24k - 8j) + (-5k + i) + (-10j - 6i)
a×b = -5i - 18j - 29k
Then
b×a = -(a×b) = 5i + 18j + 29k
