SOLUTION: A hot-air balloon rises from the ground with a velocity of (2.00 m/s )y-direction. A champagne bottle is opened to celebrate takeoff, expelling the cork horizontally with a velocit

Question 507053: A hot-air balloon rises from the ground with a velocity of (2.00 m/s )y-direction. A champagne bottle is opened to celebrate takeoff, expelling the cork horizontally with a velocity of (4.00 m/s )x-direction relative to the balloon. When opened, the bottle is 7.00 m above the ground. What is the maximum height above the ground attained by the cork (what is the ymax)?
I have this so far:
x(t)=4t
v(t)=4
y(t)= 7+ 2t -0.59.81t^2
vy(t)= 2-9.81t
Not sure where to go next
Please help
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the vertical equation (the y-direction) is ___ y = -(1/2)gt^2 + vt + y0 ___ or ___ y = -4.9t^2 + 2t + 7

ymax occurs on the axis of symmetry of the parabolic equation ___ t = -(2) / [2(-4.9)]
___ calculate t and substitute into the equation to find ymax

analytically, it takes about 1/5 sec for the upward velocity to go to zero
___ during which time the distance traveled is about 1/5 m
___ so ymax is about 7.2 m
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