NSAA 2017 Advanced Mathematics And Advanced Physics S1

• A.$-\frac{3}{4}$
• B.$\frac{3}{4}$
• C.$-\frac{3\sqrt{3}}{4}$
• D.$\frac{3\sqrt{3}}{4}$
• E.$\frac{3-\sqrt{3}}{4}$
• F.$\frac{3}{4}-\sqrt{3}$
• G.$-\frac{\sqrt{3}}{2}$
• H.$\frac{\sqrt{3}}{2}$

Answer: E

The diagram shows a crane being used on a building site. The crane is perfectly balanced about P.

The load is now moved to the left by 5.0 m.

To keep the crane perfectly balanced about P, how far does the counterweight have to move, and in which direction?

(gravitational field strength = $10\,\mathrm{N}\,\mathrm{kg}^{-1}$)

• A.1.0 m to the left
• B.1.0 m to the right
• C.3.0 m to the left
• D.3.0 m to the right
• E.4.0 m to the left
• F.4.0 m to the right

Answer: B

• A.0
• B.2
• C.3
• D.4
• E.8

Answer: C

• A.It is parallel to its motion.
• B.It is perpendicular to its motion.
• C.It is zero.
• D.It is equal to its weight.
• E.It is equal to the drag acting on the aircraft.

Answer: C

• A.$\log_2 3$
• B.$\log_3 2$
• C.2
• D.$\log_{10} 2$
• E.$\frac{2}{3}$

Answer: B

• A.$16.0\,\mathrm{ms}^{-1}$
• B.$20.0\,\mathrm{ms}^{-1}$
• C.$25.6\,\mathrm{ms}^{-1}$
• D.$32.0\,\mathrm{ms}^{-1}$
• E.$36.2\,\mathrm{ms}^{-1}$
• F.$39.3\,\mathrm{ms}^{-1}$

Answer: D

• A.$p=-3$ and $q=-8$
• B.$p=-3$ and $q=8$
• C.$p=3$ and $q=-8$
• D.$p=-9$ and $q = 24$
• E.$p=9$ and $q = 24$
• F.$p=9$ and $q=-24$

Answer: D

A block of mass 1.0 kg is at rest on a rough horizontal surface. The block is attached by a light inextensible string to a force meter. The other end of the force meter is attached by another light inextensible string via a frictionless pulley to a load of mass 1.0 kg. The block remains stationary.

What is the reading on the force meter?

(gravitational field strength = $10\,\mathrm{N}\,\mathrm{kg}^{-1}$)

• A.0.0 N
• B.0.5 N
• C.1.0 N
• D.2.0 N
• E.5.0 N
• F.10 N
• G.20 N

Answer: F

• A.240
• B.4320
• C.4860
• D.12960
• E.19440

Answer: E

• A.0.80 J
• B.3.6 J
• C.4.0 J
• D.7.2 J
• E.8.0 J

Answer: A

• A.$\frac{13}{12}\pi, \frac{17}{12}\pi$
• B.$\frac{7}{6}\pi, \frac{4}{3}\pi$
• C.$\frac{7}{6}\pi, \frac{11}{6}\pi$
• D.$\frac{5}{4}\pi, \frac{7}{4}\pi$
• E.there are no values of x in this range

Answer: A

A stone is fired vertically upwards at a speed of $13\,\mathrm{ms}^{-1}$ on a still day from the top of a $6.0\,\mathrm{m}$ high cliff. It then falls down and lands at the bottom of the cliff.

From when the stone passes the top of the cliff on the way down, how long does it take to reach the ground at the bottom of the cliff?

(air resistance can be ignored; gravitational field strength = $10\,\mathrm{N}\,\mathrm{kg}^{-1}$)

• A.0.40 s
• B.$\frac{6.0}{6.5}\,\mathrm{s}$
• C.0.60 s
• D.$\sqrt{1.2}\,\mathrm{s}$
• E.1.3 s
• F.2.0 s
• G.2.5 s
• H.3.0 s

Answer: A

• A.-10
• B.-2
• C.-1
• D.8
• E.26

Answer: C

An archer fires an arrow of mass 0.024 kg vertically upwards from a bow.

The graph shows how the force of the bowstring on the arrow varies with distance as the arrow moves upwards.

The work done by the force of the bowstring is given by the area under the force-distance graph.

When the arrow leaves the bow, what is the kinetic energy of the arrow, and what is the maximum height that it gains from this point?

(Air resistance can be ignored. The effect of gravity as the arrow is fired is negligible compared to the force of the bowstring. The gravitational field strength = $10\,\mathrm{N}\,\mathrm{kg}^{-1}$.)

• A.kinetic energy / J: 38.4, height / m: 16
• B.kinetic energy / J: 38.4, height / m: 160
• C.kinetic energy / J: 38.4, height / m: 1600
• D.kinetic energy / J: 38.4, height / m: 16000
• E.kinetic energy / J: 76.8, height / m: 32
• F.kinetic energy / J: 76.8, height / m: 320
• G.kinetic energy / J: 76.8, height / m: 3200
• H.kinetic energy / J: 76.8, height / m: 32000

Answer: B

• A.$x<0, x>4$
• B.$0<x<4$
• C.$0<x<1, x>4$
• D.$x<0, 1<x<4$
• E.$x<1, x>4$
• F.$1<x<4$

Answer: A

A book of mass $m$ rests on a rough horizontal surface. The surface is now tilted as shown:

When the angle of tilt $\theta$ is 20°, the book slides down the slope at a constant speed.

What is the acceleration of the book down the slope when the angle of tilt is 25°?

(gravitational field strength = $g$)

• A.$g (\cos 20° - \sin 20° \tan 5°)$
• B.$g (\cos 20° - \sin 20° \tan 25°)$
• C.$g (\cos 25° - \sin 5° \tan 20°)$
• D.$g (\cos 25° - \sin 25° \tan 20°)$
• E.$g (\sin 20° - \cos 20° \tan 5°)$
• F.$g (\sin 20° - \cos 20° \tan 25°)$
• G.$g (\sin 25° - \cos 5° \tan 20°)$
• H.$g (\sin 25° - \cos 25° \tan 20°)$

Answer: H

• A.2.00
• B.1.75
• C.1.50
• D.1.00
• E.-0.25
• F.-0.50

Answer: B

The graph shows how the horizontal force on a tennis ball of mass $m$ varies during a shot in a tennis match. The ball is initially travelling horizontally toward the racket with speed $u$ and leaves the racket horizontally travelling in the opposite direction with speed $v$.

Which expression gives the magnitude of the momentum of the ball as it leaves the racket?

• A.$F(t_2-t_1)$
• B.$F(t_2-t_1) - mu$
• C.$F(t_2-t_1) + mu$
• D.$mv - mu$
• E.$Ft_2 - mu$

Answer: B