[Maximum number: 1]

Instantaneous velocity is defined as...

A

$\frac{\text { displacement }}{\text { time taken }}$ .

B

rate of change of position.

C

$\frac{\text { distance moved }}{\text { time taken }}$ .

D

rate of change of distance.

[Maximum number: 1]

A group of students is trying to determine the density and the viscosity of a liquid.

To determine the density, they use a balance to read the mass m of a sphere in air and immersed in the liquid.

They use a sphere of volume $V=1.827 \times 10^{-7} \mathrm{~m}^{3}$ .
The readings are $m_{\text {air }}=1.427 \mathrm{~g}$ in air and $m_{\text {lmmersed }}=1.208 \mathrm{~g}$ in the liquid.
The readings are different due to buoyancy. The buoyancy force $F_{\mathrm{b}}$ is given by

F_{\mathrm{b}}=\rho V g

where V is the volume of the sphere and $\rho$ is the density of the liquid.

(a)

Outline how the students may verify that the sphere reaches terminal velocity.

They repeat the experiment several times and estimate an average for

v_{\mathrm{t}}=(0.71 \pm 0.05) \mathrm{ms}^{-1}

They use the equation

\eta=\frac{m_{\mathrm{air}} g-\rho V g}{6 \pi r v_{\mathrm{t}}}

where
r= radius of the sphere,
$v_{\mathrm{t}}=$ terminal velocity of the sphere,
$\eta=$ viscosity of the liquid.
The radius r of the sphere is 3.520 mm .

[ 1 ]

[Maximum number: 3]

A tennis ball is hit with a racket from a point 1.5 m above the floor. The ceiling is 8.0 m above the floor. The initial velocity of the ball is $15 \mathrm{~m} \mathrm{~s}^{-1}$ at $50^{\circ}$ above the horizontal. Assume that air resistance is negligible.

(a)

Determine whether the ball will hit the ceiling.

[ 3 ]

[Maximum number: 3]

A tennis ball is hit with a racket from a point 1.5 m above the floor. The ceiling is 8.0 m above the floor. The initial velocity of the ball is $15 \mathrm{~m} \mathrm{~s}^{-1}$ at $50^{\circ}$ above the horizontal. Assume that air resistance is negligible.

(a)

Determine whether the ball will hit the ceiling.

[ 3 ]

[Maximum number: 5]

A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest by a cable pulled by a motor that exerts a horizontal force on the glider throughout the launch.

(a)

The glider reaches its launch speed of $27.0 \mathrm{~m} \mathrm{~s}^{-1}$ after accelerating for 11.0 s . Assume that the glider moves horizontally until it leaves the ground. Calculate the total distance travelled by the glider before it leaves the ground.

[ 2 ]

(b)

At a particular instant in the flight the glider is losing 1.00 m of vertical height for every 6.00 m that it goes forward horizontally. At this instant, the horizontal speed of the glider is $12.5 \mathrm{~m} \mathrm{~s}^{-1}$ . Calculate the velocity of the glider. Give your answer to an appropriate number of significant figures.

[ 3 ]

[Maximum number: 2]

A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest by a cable pulled by a motor that exerts a horizontal force on the glider throughout the launch.

(a)

The glider reaches its launch speed of $27.0 \mathrm{~m} \mathrm{~s}^{-1}$ after accelerating for 11.0 s . Assume that the glider moves horizontally until it leaves the ground. Calculate the total distance travelled by the glider before it leaves the ground.

[ 2 ]

[Maximum number: 2]

An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.

The unextended length of the rope is 60.0 m . From position A to position B, the block falls freely.

(a)

At position B the rope starts to extend. Calculate the speed of the block at position B.

[ 2 ]

[Maximum number: 2]

The graph shows the variation with time t of the horizontal force F exerted on a tennis ball by a racket.

The tennis ball was stationary at the instant when it was hit. The mass of the tennis ball is $5.8 \times 10^{-2} \mathrm{~kg}$ . The area under the curve is 0.84 Ns .

(a)

Draw a graph to show the variation with t of the horizontal speed v of the ball while it was in contact with the racket. Numbers are not required on the axes.

[ 2 ]

[Maximum number: 5]

A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of $64 \mathrm{~m} \mathrm{~s}^{-1}$ . The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms .

(a)

The student strikes the tennis ball at point P . The tennis ball is initially directed at an angle of $7.00^{\circ}$ to the horizontal.

The following data are available.

[ 5 ]

(i)

Calculate the time it takes the tennis ball to reach the net.

[ 2 ]

(ii)

Show that the tennis ball passes over the net.

[ 3 ]

[Maximum number: 2]

In an experiment to measure the acceleration of free fall a student ties two different blocks of masses $m_{1}$ and $m_{2}$ to the ends of a string that passes over a frictionless pulley.

The student calculates the acceleration a of the blocks by measuring the time taken by the heavier mass to fall through a given distance. Their theory predicts that $a=g \frac{m_{1}-m_{2}}{m_{1}+m_{2}}$ and this can be re-arranged to give $g=a \frac{m_{1}+m_{2}}{m_{1}-m_{2}}$ .

(a)

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain,

[ 2 ]

(i)

the advantage with reference to the magnitude of the acceleration that is obtained.

[ 2 ]