A car of mass $$$1600 \mathrm{~kg}$$$ is pulling a caravan of mass $$$800 \mathrm{~kg}$$$. The car and the caravan are connected by a light rigid tow-bar. The resistances to the motion of the car and caravan are $$$400 \mathrm{~N}$$$ and $$$250 \mathrm{~N}$$$ respectively. The car and caravan now travel up a straight hill, inclined at an angle of $$$\sin ^{-1} 0.05$$$ to the horizontal, at a constant speed of $$$v \mathrm{~m} \mathrm{~s}^{-1}$$$. The car's engine is working at $$$32.5 \mathrm{~kW}$$$. Find $$$v$$$ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_43 Year：2020 Question No：6(b)

Answer:

$[\mathrm{DF}=650+2400 \times 10 \times 0.05]$
$32500=(650+24000 \times 0.05) v$
$v=17.6$

Knowledge points:

4.1.3 use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero （Solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions.）

4.5.4 use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion Including calculation of (average) power;P = Fv

Answer:

Knowledge points:

Solution:

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