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### ELOUISE STIDHAM

#### Cambridge International AS and A Level

 Name of student ELOUISE STIDHAM Date Adm. number 0 Year/grade Stream Subject Mechanics 2 (M2) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 9 7 9 7 7 9 48
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/51/M/J/12/5, Topic: - A particle$P$of mass$0.4 \mathrm{~kg}$is released from rest at the top of a smooth plane inclined at$30^{\circ}$to the horizontal. The motion of$P$down the slope is opposed by a force of magnitude$0.6 x \mathrm{~N}$, where$x \mathrm{~m}$is the distance$P$has travelled down the slope.$P$comes to rest before reaching the foot of the slope. Calculate$\text{(i)}$the greatest speed of$P$during its motion,$\text{(ii)}$the distance travelled by$P$during its motion.$$Question 2 Code: 9709/52/M/J/12/5, Topic: - A ball is projected with velocity$25 \mathrm{~m} \mathrm{~s}^{-1}$at an angle of$70^{\circ}$above the horizontal from a point$O$on horizontal ground. The ball subsequently bounces once on the ground at a point$P$before landing at a point$Q$where it remains at rest. The distance$P Q$is$17.1 \mathrm{~m}$.$\text{(i)}$Calculate the time taken by the ball to travel from$O$to$P$and the distance$O P$.$\text{(ii)}$Given that the horizontal component of the velocity of the ball does not change at$P$, calculate the speed of the ball when it leaves$P$.$$Question 3 Code: 9709/53/M/J/12/5, Topic: - A light elastic string has natural length$3 \mathrm{~m}$and modulus of elasticity$45 \mathrm{~N}$. A particle$P$of mass$0.6 \mathrm{~kg}$is attached to the mid-point of the string. The ends of the string are attached to fixed points$A$and$B$which lie on a line of greatest slope of a smooth plane inclined at$30^{\circ}$to the horizontal. The distance$A B$is$4 \mathrm{~m}$, and$A$is higher than$B$.$\text{(i)}$Calculate the distance$A P$when$P$rests on the slope in equilibrium.$P$is released from rest at the point between$A$and$B$where$A P=2.5 \mathrm{~m}$.$\text{(ii)}$Find the maximum speed of$P$.$\text{(iii)}$Show that$P$is at rest when$A P=1.6 \mathrm{~m}$.$$Question 4 Code: 9709/51/O/N/12/5, Topic: - A particle$P$is projected with speed$30 \mathrm{~m} \mathrm{~s}^{-1}$at an angle of$60^{\circ}$above the horizontal from a point$O$on horizontal ground. For the instant when the speed of$P$is$17 \mathrm{~m} \mathrm{~s}^{-1}$and increasing,$\text{(i)}$show that the vertical component of the velocity of$P$is$8 \mathrm{~m} \mathrm{~s}^{-1}$downwards,$\text{(ii)}$calculate the distance of$P$from$O$.$$Question 5 Code: 9709/52/O/N/12/5, Topic: - Question 6 Code: 9709/53/O/N/12/5, Topic: - A small ball$B$of mass$0.2 \mathrm{~kg}$is attached to fixed points$P$and$Q$by two light inextensible strings of equal length.$P$is vertically above$Q$, the strings are taut and each is inclined at$60^{\circ}$to the vertical.$B$moves with constant speed in a horizontal circle of radius$0.6 \mathrm{~m}$.$\text{(i)}$Given that the tension in the string$P B$is$7 \mathrm{~N}$, calculate$\text{(a)}$the tension in string$Q B$,$\text{(b)}$the speed of$B$.$\text{(ii)}$Given instead that$B$is moving with angular speed$7 \mathrm{rad} \mathrm{s}^{-1}$, calculate the tension in the string$Q B$.$\$

Worked solutions: P1, P3 & P6 (S1)

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