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Vectors & Physics?
A cart is propelled over an xy plane with acceleration components ax = 5.5 m/s2 and ay = -2.0 m/s2. Its initial velocity has components v0x = 8.0 m/s and v0y = 14 m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate?
v = ( i + j ) m/s
2 Answers
- JicotilloLv 61 decade agoFavorite Answer
Note vertical acceleration is negative. And since the vertical component of the initial velocity is positive, this means that eventually vertical velocity becomes zero. This is the point of greatest y coordinate; from this point on, y coordinate will monotonically decrease. From vy = v₀y + at, find the time for maximum y displacement:
t = -14 m/s / -2 m/s² = 7 s.
What follows is plain routine:
vy(7) = 0, as explained above.
vx(7) = v₀x + at = 8 m/s + 5.5 m/s² × 7 s = 46.5 m/s.
The vector sought: v = (46.5 i + 0 j)
- Anonymous1 decade ago
Solve each axis independently using the customary formulas, and then simply express the result in vector form.
