Current, I got it right on my quiz
Answer:
magnitude = 3
unit vector = 
Explanation:
Given vectors:
u = 2i + 2j - k
v = -i + k = -i + 0j + k
(a) u x v is the cross product of u and v, and is given by;
u x v = i(2+0) - j(2 - 1) + k(0 - 2)
u x v = 2i - j - 2k
Now the magnitude of u x v is calculated as follows:
| u x v | = 
| u x v | = 
| u x v | = 
| u x v | = 3
Therefore, the magnitude of u x v is 3
(b) The unit vector û parallel to u x v in the direction of u x v is given by the ratio of u x v and the magnitude of u x v. i.e
û =
u x v = 2i - j - 2k [<em>calculated in (a) above</em>]
|u x v| = 3 [<em>calculated in (a) above</em>]
∴ û = 
∴ û = 
Given that,
The acceleration of gravity is -9.8 m/s²
Initial velocity, u = 39.2 m/s
Time, t = 2 s
To find,
The final velocity of the shot.
Solution,
Let v is the final velocity of sling shot. Using first equation of motion to find it.
v = u +at
Here, a = -g
v = u-gt
v = (39.2)-(9.8)(2)
v = 19.6 m/s
So, its velocity after 2 seconds is 19.6 m/s.