Q49. A helicopter is ascending vertic... [FREE SOLUTION]

Chapter 2: Q49. (page 45)

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 v₀ for the package?]

Short Answer

Expert verified

The obtained solution is $t = 4.108 s$ .

Step by step solution

Step 1. Kinematic equations

Kinematics is one of the subfields of physics that describes the movement of a certain component without considering force.

Given data.

The speed of the helicopter is $v = 5.40 m / s$ .

The height above the Earth is $h = 105 m$ .

The relation from the equation of motion is given by.

$\begin{matrix} h = v t + \frac{1}{2} g t^{2} \\ t^{2} + 2 \frac{v}{g} t - \frac{2 h}{g} = 0 \end{matrix}$

Here, g is the gravitational acceleration, and t is the time.

On plugging the values in the above relation, you get.

$\begin{matrix} t^{2} + 2 (\frac{5.40 m / s}{- 9.81 m / s^{2}}) t - \frac{2 (- 105 m)}{- 9.81 m / s^{2}} = 0 \\ t^{2} + 1.1 t - 21.4 = 0 \end{matrix}$

Step 2. Calculation of time

On solving the above equation, you get;

$\begin{array}{l} t = \frac{- 1.1 卤 \sqrt{{(1.1)}^{2} - 4 (1) (- 21.4)}}{2 脳 1} \\ t = 4.108 鈥� s, - 5.208 鈥� s \end{array}$

Thus, $t = 4.108 鈥� s$ is the required time of the helicopter.

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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 v₀ for the package?]

Short Answer

Step by step solution

Step 1. Kinematic equations

Step 2. Calculation of time

One App. One Place for Learning.

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91影视

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 v0 for the package?]

Short Answer

Step by step solution

Step 1. Kinematic equations

Step 2. Calculation of time

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Torque and Rotational Motion

Wave Optics

Fields in Physics

Radiation

Modern Physics

Study anywhere. Anytime. Across all devices.

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 v₀ for the package?]