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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

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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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