# Dynamics Question #4

## Homework Statement

An aeroplane of mass 20 tonne lands on an aircraft carrier with a horizontal velocity of $$80ms^{-1}$$. A $$100m$$ runway is available.
(a) What must be the acceleration to bring the aeroplane to rest safely?
(b) What retarding force is requires?

## Homework Equations

$$v^2 = u^2 + 2as$$
$$F = m.a$$

## The Attempt at a Solution

$$m = 90 \times 10^3kg \ , \ v = 80ms^{-1} \ , \s = 100m$$

(a) $$v^2 = u^2 + 2as$$
$$0^2 = 80^2 + 2 \times a \times 100$$
$$-80^2 = 200a$$
$$a = \frac{-80^2}{200}$$
$$a = -32ms^{-2}$$

(b) $$F = m.a$$
$$F = 90 \times 10^3 \times -32$$
$$F = -2.9 \times 10^6 N$$

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