Question

An aero plane starts from rest with an acceleration 0f 2m/s 2 and takes a run for 50s before taking off. What is the minimum length of the runway and with what velocity the plane took off ?
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Answer 1

Given :-

• Initial velocity (u) = $\sf\red{0m/s}$
• Acceleration (a) = $\sf\orange{2m/s^2}$
• Time taken (t) = $\sf\blue{50s}$

To Find:-

• $\sf\purple{Final \ velocity \ (v)}$
• $\sf\green{Length \ of \ runway}$

Solution:-

Using 1st equation of motion

$\to\:\:\sf{ v = u+at}$

$\to\:\:\sf{ v = 0+ 2\times 50}$

$\to\:\:\sf{ v = 100m/s}$

∴ Final velocity of the aeroplane is $\bf \red{100m/s}$

Now, Calculating the length of runway.

For that we need to use 3rd equation of motion.

$\to\:\:\sf{ v^2 = u^2 +2as}$

$\to\:\:\sf{ 100^2 = 0^2 + 2\times 2\times s}$

$\to\:\:\sf{ 10000 = 4\times s}$

$\to\:\:\sf{ 4 \times s = 10000}$

$\to\:\:\sf{ s = \dfrac{10000}{4}}$

$\to\:\:\sf{ s = 2500}$

$\to\:\:\sf{ s = \dfrac{2500}{1000}}$

$\to\:\:\sf{s = 2.5km}$

☆ Length of the runway is $\bf\red{2.5km}$