(II) A helicopter is ascending vertically with a speed of...

(II) A helicopter is ascending vertically with a speed of 5.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [$Hint$: What is $\upsilon_0$ for the package?]

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Key Concepts

Uniformly Accelerated Motion

This concept refers to motion under a constant acceleration, such as gravity. The equations of motion, which relate displacement, initial velocity, time, and acceleration, are used to compute various kinematic parameters, including the time taken for an object in free fall to cover a given displacement.

Initial Velocity

Initial velocity is the speed and direction at which an object starts its motion. In cases where an object is released from a moving platform like a helicopter, it retains the velocity of that platform at the moment of release, which is a crucial factor in accurately determining its subsequent motion.

Projectile Motion

Projectile motion involves objects moving under the influence of gravity after being given an initial velocity. Even when an object is simply dropped from a moving vehicle, its motion is considered projectile motion, as it continues with its initial velocity while also experiencing gravitational acceleration.

Quadratic Equation

When applying the kinematic equations to determine the time of flight or displacement in accelerated motion, the relationship often takes the form of a quadratic equation. Solving this quadratic equation using the quadratic formula is essential to find the physically meaningful solution for time.

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