A helicopter is flying in a straight line over a level field...

A helicopter is flying in a straight line over a level field at a constant speed of 6.20 $\mathrm{m} / \mathrm{s}$ and at a constant altitude of 9.50 $\mathrm{m}$ . A package is ejected horizontally from the helicopter with an initial velocity of 12.0 $\mathrm{m} / \mathrm{s}$ relative to the helicopter and in a direction opposite the helicopter's motion. (a) Find the initial speed of the package relative to the ground. (b) What is the horizontal distance between the helicopter and the package at the instant the package strikes the ground? (c) What angle does the velocity vector of the package make with the ground at the instant before impact, as seen from the ground?

A helicopter is flying in a straight line over a level field at a constant speed of 6.20 $\mathrm{m} / \mathrm{s}$ and at a constant altitude of 9.50 $\mathrm{m}$ .
A package is ejected horizontally from the helicopter with an
initial velocity of 12.0 $\mathrm{m} / \mathrm{s}$ relative to the helicopter and in a direction opposite the helicopter's motion. (a) Find the initial speed of the package relative to the ground. (b) What is the horizontal distance between the helicopter and the package at the
instant the package strikes the ground? (c) What angle does the
velocity vector of the package make with the ground at the instant before impact, as seen from the ground?

Key Concepts

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They are used to calculate displacement, velocity, and time for each component of the motion. For projectile motion, these equations help determine how long an object remains in the air and how far it travels horizontally before landing.

Vector Decomposition

Vector decomposition is the process of breaking a vector into its horizontal and vertical components. This is crucial when analyzing motion in two dimensions, as it allows one to apply separate kinematic equations to each component independently, thereby simplifying the problem-solving process.

Projectile Motion

Projectile motion is the two-dimensional motion of an object under the influence of gravity, where the only acceleration acting on the object is due to gravity. This concept involves analyzing the motion separately in the horizontal and vertical directions, with the horizontal component typically having constant velocity and the vertical component experiencing constant acceleration.

Relative Velocity

Relative velocity refers to the calculation of an object's velocity as observed from a particular frame of reference. In problems involving multiple moving bodies, such as a package being ejected from a moving helicopter, it is necessary to add or subtract velocities vectorially to determine the true speed and direction relative to the ground.

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