An aircraft has a liftoff speed of 120km/h

Question:

A Cessna aircraft has a liftoff speed of 120 km/h.

(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240 m?

(b) How long does it take the aircraft to become airborne?

Equation of Motion:

Considering uniformly accelerated motion, a body with initial velocity u is moving linearly with uniform acceleration a covers a distance s in some time t .

The equation which determines the final velocity v of the body and the distance s travelled by the body is given by

{eq}v=u+at\\ v^2=u^2+2as {/eq}

.

Answer and Explanation: 1

Given:

• The initial speed of the aircraft is {eq}u =0 {/eq} as it starts from rest.

• The final takeoff speed of the aircraft is {eq}v=120 \ km/h =...

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Solving Kinematics Problems

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Chapter 2 / Lesson 21

Kinematics problems analyze classical mechanics of motion using four standard mathematical equations. Learn the use of these equations to solve kinematics problems using math.

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Question:

A Cessna aircraft has a lift-off speed of 120 km/h. What minimum constant acceleration does the aircraft require if the aircraft is to be airborne after a takeoff run of 290 m?

When an object starts its motion from the rest position the initial velocity of the object is zero. Acceleration is defined both in direction and magnitude so it is a vector quantity. In the SI unit measurement system, the acceleration of an object is described in {eq}(\text{m/s}^{2}) {/eq}

Answer and Explanation: 1

We are given the following data:

• Lift speed of aircraft, {eq}v=120\ \text{km/h} {/eq}

• Runway distance, {eq}s=290\ \text{m} {/eq}

• Inital velocity...

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Speed, Velocity & Acceleration

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Chapter 47 / Lesson 5

Learn about the speed, velocity, and acceleration of an object in motion. Understand the relation between speed, velocity, and acceleration.

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Three Children are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and avery light board 3.6 m long. Two playmates are already on either end. Boy A has a mass of 50kg, and girl B a mass of 35 kg. Where should girl C, whose mass is 25 kg, placed herself so as to balance the seesaw.

An aircraft has a lift-off of $120km/h.$ What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of $240m?$ (in m/s$^2$)A. ${\text{2}}{\text{.2}}$B. ${\text{2}}{\text{.3}}$C. ${\text{2}}{\text{.4}}$D. ${\text{2}}{\text{.5}}$

Answer

Verified

Hint: First convert the units of the given terms in the same format. So, convert kilometre per hour in metres per second. From the given terms find the unknown term acceleration from the correlation. Use the difference of the initial velocity and final velocity equation of the motion.

Complete step by step answer:
Here, the initial velocity of an aircraft be $u = 0m/s$
Final velocity of an aircraft, $v = 120km/h = \dfrac{{120 \times 1000}}{{3600}} = 33.33m/s$
Run off distance, $s = 240m$
Now, using the equation –
${v^2} - {u^2} = 2as$
Place the known values in the above equation –
${\left( {33.33} \right)^2} - {0^2} = 2a(240)$
Simplify and make unknown acceleration “a” the subject –
$
  a = \dfrac{{{{(33.33)}^2}}}{{2(240)}} \\
  a = 2.3m/{s^2} \\
 $
Therefore, the required answer is – the minimum constant acceleration $a = 2.3m/{s^2}$ aircraft requires if it is to be airborne after a takeoff run of $240m$.

So, the correct answer is “Option B”.

Note:
Remember all the three laws of motion and its equation to solve these types of word problems. Always double check the given units and units of the answer required in the solution. Always know the basic relation among the different physical parameters to convert its units. Like kilometres to metres, kilogram to gram, milli-second to second and many such relations.