As a runaway scientific balloon ascends at 19.6 m / s, one of its instrument packages breaks fr

step 1 In this problem of motion in a straight line we have given a figure I'm showing you first. So th

As a runaway scientific balloon ascends at 19.6 m / s, one...

As a runaway scientific balloon ascends at $19.6 \mathrm{~m} / \mathrm{s},$ one of its instrument packages breaks free of a harness and free-falls. Figure 2 - 34 gives the vertical velocity of the package versus time, from before it breaks free to when it reaches the ground. (a) What maximum height above the break-free point does it risc? (b) How high is the break-free point above the ground?

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Key Concepts

Kinematic Equations

These equations relate displacement, velocity, acceleration, and time for bodies moving with constant acceleration. They allow for the prediction of future positions and speeds and are fundamental tools for analyzing motions such as objects in free-fall or thrown vertically under gravity.

Projectile Motion

This concept describes the motion of an object launched into the air where its path, or trajectory, is governed primarily by the effects of gravity. Even with an initial upward velocity, the object will decelerate under gravity until its velocity is zero at the peak, and then accelerate downward, following a predictable path.

Acceleration Due to Gravity

This is the constant rate at which objects accelerate toward the Earth when in free-fall, typically approximated as 9.8 m/s². It is the key factor determining how quickly the upward motion slows and the subsequent downward motion speeds up in the absence of other forces.

Velocity-Time Graph Analysis

By plotting an object's velocity against time, one can visually interpret different phases of motion. The slope of the graph indicates acceleration, and the area under the curve corresponds to displacement. This method is especially useful for understanding how and when an object reaches its maximum height and the distance it travels during its motion.

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