Question: A hot-air balloon is ascending at the rate of and role="math" localid="1662959960903" is above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?
Initial speed for package,
Height from which package is dropped
The problem deals with the kinematic equation of motion in which the motion of an object is described at constant acceleration. Using the Kinematic equation, the velocity and time to reach the ground dropped from hot air balloon at height can be calculated.
The velocity in kinematic equation is expressed as,
(ii) 41 m/s
Consider downward as positive and upward as negative.
Calculate velocity (Part b), which can then be used in the calculation of time.
The balloon is ascending at the rate of -12m/s, and the package is dropped over the side.
Using equation (i), the final velocity will be
The velocity of the package when it hits the ground is 41.38 m/s
Using equation (ii),
The time taken by the packet to reach the ground is 5.45sec.
The Zero Gravity Research Facility at the NASA Glenn Research Center includes a drop tower. This is an evacuated vertical tower through which, among other possibilities, a diameter sphere containing an experimental package can be dropped. (a) How long is the sphere in free fall? (b) What is its speed just as it reaches a catching device at the bottom of the tower? (c) When caught, the sphere experiences an average deceleration of as its speed is reduced to zero. Through what distance does it travel during the deceleration?
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