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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

01

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

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

Given data.

The initial velocity is vo鈥�=鈥�0as it starts from rest.

The final velocity is v鈥�=鈥�35鈥�ms.

The acceleration of the plane is a鈥�=鈥�3.0鈥�ms2.

Assumption.

Assume that a runway of length 螖xis needed.

Now, you know that

role="math" localid="1642833471252" v2鈥�=鈥�vo2鈥�+鈥�2a鈥�螖x鈥�(i).

02

Step 2. Calculation of the length of the highway

Now, from equation (i),

v2鈥�=鈥�vo2鈥�+鈥�2a鈥�螖x35鈥�ms2鈥�=鈥�0鈥�ms2鈥�+鈥�2鈥�脳鈥�3.0鈥�ms2鈥�脳鈥�螖x6.0鈥�ms2鈥�脳鈥�螖x鈥�=鈥�35鈥�ms2鈥�螖x鈥�=鈥�204.2鈥�m

Therefore, a runway of length 204.2 m is needed.

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