Chapter 2: Q24. (page 44)

A light plane must reach a speed of 35 m/s for takeoff. What length of a runway is needed if the (constant) acceleration is 3.0 m/s²?

Short Answer

Expert verified

A runway of length 204.2 m is needed.

Step by step solution

Step 1. Relation between initial velocity, final velocity, acceleration, and displacement

The rate of change in the object’s displacement is known as the object’s velocity. It has both direction and magnitude.

Given data.

The initial velocity is $v_{o} = 0$ as it starts from rest.

The final velocity is $v_{} = 35 \frac{m}{s}$ .

The acceleration of the plane is $a = 3.0 \frac{m}{s^{2}}$ .

Assumption.

Assume that a runway of length $Δ x$ is needed.

Now, you know that

role="math" localid="1642833471252" $v^{2} = v_{o}^{2} + 2 a Δ x \dots (i)$ .

Step 2. Calculation of the length of the highway

Now, from equation (i),

$\begin{matrix} v^{2} = v_{o}^{2} + 2 a Δ x \\ {(35 \frac{m}{s})}^{2} = {(0 \frac{m}{s})}^{2} + 2 \times 3.0 \frac{m}{s^{2}} \times Δ x \\ 6.0 \frac{m}{s^{2}} \times Δ x = {(35 \frac{m}{s})}^{2} \\ Δ x = 204.2 m \end{matrix}$

Therefore, a runway of length 204.2 m is needed.

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A light plane must reach a speed of 35 m/s for takeoff. What length of a runway is needed if the (constant) acceleration is 3.0 m/s²?

Short Answer

Step by step solution

Step 1. Relation between initial velocity, final velocity, acceleration, and displacement

Step 2. Calculation of the length of the highway

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A light plane must reach a speed of 35 m/s for takeoff. What length of a runway is needed if the (constant) acceleration is 3.0 m/s2?

Short Answer

Step by step solution

Step 1. Relation between initial velocity, final velocity, acceleration, and displacement

Step 2. Calculation of the length of the highway

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Modern Physics

Classical Mechanics

Linear Momentum

Space Physics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

A light plane must reach a speed of 35 m/s for takeoff. What length of a runway is needed if the (constant) acceleration is 3.0 m/s²?