Answer:
176.44 m
Explanation:
y = (vertical vi)t + (1/2)gt^2
315 = 0 + (1/2)(9.8)t^2
t = 8.02s
x = (horizontal vi)t + (1/2)at^2
x = (22)(8.02) + 0
x = 176.44 m
F = ma
3900 = 300a
a = 3900÷300
a = 13m/s/s
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
