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### HENRYTAIGO

#### Cambridge International AS and A Level

 Name of student HENRYTAIGO Date Adm. number Year/grade HenryTaigo Stream HenryTaigo Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 6 7 7 6 6 8 40
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/41/M/J/16/4, Topic: - Coplanar forces of magnitudes$50 \mathrm{~N}, 48 \mathrm{~N}, 14 \mathrm{~N}$and$P \mathrm{~N}$act at a point in the directions shown in the diagram. The system is in equilibrium. Given that tan$\alpha=\frac{7}{24}$, find the values of$P$and$\theta$.$[6]$Question 2 Code: 9709/42/M/J/16/4, Topic: - A sprinter runs a race of$400 \mathrm{~m}$. His total time for running the race is$52 \mathrm{~s}$. The diagram shows the velocity-time graph for the motion of the sprinter. He starts from rest and accelerates uniformly to a speed of$8.2 \mathrm{~m} \mathrm{~s}^{-1}$in$6 \mathrm{~s}$. The sprinter maintains a speed of$8.2 \mathrm{~m} \mathrm{~s}^{-1}$for$36 \mathrm{~s}$, and he then decelerates uniformly to a speed of$V \mathrm{~m} \mathrm{~s}^{-1}$at the end of the race.$\text{(i)}$Calculate the distance covered by the sprinter in the first$42 \mathrm{~s}$of the race.$[2]\text{(ii)}$Show that$V=7.84$.$[3]\text{(iii)}$Calculate the deceleration of the sprinter in the last$10 \mathrm{~s}$of the race.$[2]$Question 3 Code: 9709/43/M/J/16/4, Topic: - A particle of mass$15 \mathrm{~kg}$is stationary on a rough plane inclined at an angle of$20^{\circ}$to the horizontal. The coefficient of friction between the particle and the plane is$0.2$. A force of magnitude$X \mathrm{~N}$acting parallel to a line of greatest slope of the plane is used to keep the particle in equilibrium. Show that the least possible value of$X$is$23.1$, correct to 3 significant figures, and find the greatest possible value of$X$.$[7]$Question 4 Code: 9709/41/O/N/16/4, Topic: - Three coplanar forces of magnitudes$F \mathrm{~N}, 2 F \mathrm{~N}$and$15 \mathrm{~N}$act at a point$P$, as shown in the diagram. Given that the forces are in equilibrium, find the values of$F$and$\alpha$.$[6]$Question 5 Code: 9709/42/O/N/16/4, Topic: - A girl on a sledge starts, with a speed of$5 \mathrm{~m} \mathrm{~s}^{-1}$, at the top of a slope of length$100 \mathrm{~m}$which is at an angle of$20^{\circ}$to the horizontal. The sledge slides directly down the slope.$\text{(i)}$Given that there is no resistance to the sledge's motion, find the speed of the sledge at the bottom of the slope.$[3]\text{(ii)}$It is given instead that the sledge experiences a resistance to motion such that the total work done against the resistance is$8500 \mathrm{~J}$, and the speed of the sledge at the bottom of the slope is$21 \mathrm{~m} \mathrm{~s}^{-1}$. Find the total mass of the girl and the sledge.$[3]$Question 6 Code: 9709/43/O/N/16/4, Topic: - A ball$A$is released from rest at the top of a tall tower. One second later, another ball$B$is projected vertically upwards from ground level near the bottom of the tower with a speed of$20 \mathrm{~m} \mathrm{~s}^{-1}$. The two balls are at the same height$1.5 \mathrm{~s}$after ball$B$is projected.$\text{(i)}$Show that the height of the tower is$50 \mathrm{~m}$.$[3]\text{(ii)}$Find the length of time for which ball$B$has been in motion when ball$A$reaches the ground. Hence find the total distance travelled by ball$B$up to the instant when ball$A$reaches the ground.$[5]\$

Worked solutions: P1, P3 & P6 (S1)

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