IB Physics HL A.1 Kinematics

[Maximum number: 7]

A student throws a ball towards a wall. The ball is released from a point 1.8 m above the ground and 8.0 m from the wall. The initial velocity of the ball makes an angle of $48^{\circ}$ with the horizontal. Air resistance is negligible.

The diagram shows the initial path of the ball. P is a point on the path.

(a)

Draw, on the diagram, an arrow to show

[ 2 ]

(i)

the velocity of the ball at P . Label this arrow v.

[ 1 ]

(ii)

the acceleration of the ball at P. Label this arrow a.

The ball takes 1.3 s to reach the wall.

[ 1 ]

(b)

Show that the initial speed of the ball is about $9 \mathrm{~ms}^{-1}$ .

[ 2 ]

horizontal velocity $v_{x}=\frac{8.0}{1.3} =6.2 \mathrm{~m} \mathrm{~s}^{-1}$ $\frac{v_{x}}{v}=\cos 48^{\circ} \Rightarrow v=\frac{8.0}{1.3 \cos 48^{\circ}}=9.2 \mathrm{m} \mathrm{~s}^{-1} \text { }$

(c)

Determine the height above the ground at which the ball hits the wall.

[ 3 ]

initial vertical velocity $v_{y}=9.2 \sin 48^{\circ}$ « $=6.8 \mathrm{~m} \mathrm{~s}^{-1}$ »
$h=1.8+\left(9.2 \sin 48^{\circ} \times 1.3\right)-\frac{1}{2} \times 9.8 \times 1.3^{2}$

2.4 «m»

Marking guidance:

Award [2 max] for h=0.6 m - candidates have not taken the initial height of 1.8m into account.

Award [2 max] for h=19 m

Award [3] for BCA

[Maximum number: 2]

A toy rocket is made from a plastic bottle that contains some water.

Air is pumped into the vertical bottle until the pressure inside forces water and air out of the bottle. The bottle then travels vertically upwards.

The air-water mixture is called the propellant.
The variation with time of the vertical velocity of the bottle is shown.

The bottle reaches its highest point at time $T_{1}$ on the graph and returns to the ground at time $T_{2}$ . The bottle then bounces. The motion of the bottle after the bounce is shown as a dashed line.

Estimate the acceleration of the bottle when it is at its maximum height.

Attempt to calculate gradient of line at $t=1.2 \mathrm{~s}$

«-» 9.8 «m s ${ }^{-2}$ » (accept 9.6-10.0)

[Maximum number: 11]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

(a)

State the significance of the negative values of s.

[ 1 ]

(b)

Use the graph to

[ 6 ]

(i)

estimate the velocity of the ball at $t=0.80 \mathrm{~s}$ .

[ 3 ]

tangent drawn to curve at 0.80 s ;
correct calculation of gradient of tangent drawn;
$-1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ or $1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ downwards;
or
correct coordinates used from the graph;
substitution into a correct equation;
$-1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ or $1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ downwards;

(ii)

calculate a value for the acceleration of free fall close to the surface of the Moon.

[ 3 ]

any correct method used;
correct reading from graph;
1.6 to $1.7 \mathrm{~m} \mathrm{~s}^{-2}$ ;

(c)

Calculate the speed of an identical ball when it falls 3.0 m from rest close to the surface of Earth. Ignore air resistance.

[ 1 ]

$\quad 7.7 \mathrm{~m} \mathrm{~s}^{-1}$ ;

(d)

Sketch, on the graph, the variation with time t of the displacement s from the point of release of the ball when the ball is dropped close to the surface of Earth.

(For this sketch take the direction towards the Earth as being negative.)

[ 3 ]

curve permanently below Moon curve;
smooth parabola;
(judge by eye)
line passing through $\mathrm{s}=-3.00 \mathrm{~m}, \mathrm{t}=0.78 \mathrm{~s}$ or $\mathrm{s}=-3.50 \mathrm{~m}, \mathrm{t}=0.84 \mathrm{~s}( \pm 1 \mathrm{~mm})$ ;

Figure for Answer to Question (d) — IB Physics HL

[Maximum number: 1]

A student throws a ball towards a wall. The ball is released from a point 1.8 m above the ground and 8.0 m from the wall. The initial velocity of the ball makes an angle of $48^{\circ}$ with the horizontal. Air resistance is negligible.

The diagram shows the initial path of the ball. P is a point on the path.

Draw, on the diagram, an arrow to show

the velocity of the ball at P . Label this arrow v.

[Maximum number: 1]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

State the significance of the negative values of s.

[Maximum number: 3]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

Use the graph to

estimate the velocity of the ball at $t=0.80 \mathrm{~s}$ .

tangent drawn to curve at 0.80 s ;
correct calculation of gradient of tangent drawn;
$-1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ or $1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ downwards;
or
correct coordinates used from the graph;
substitution into a correct equation;
$-1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ or $1.3 \pm 0.1 \mathrm{~m} \mathrm{~s}^{-1}$ downwards;

[Maximum number: 2]

This question is about the motion of a ship and observing objects from it.

The ship's engines are switched off and the ship comes to rest from a speed of $7 \mathrm{~m} \mathrm{~s}^{-1}$ in a time of 650 s .

It is unlikely that the acceleration of the ship will be uniform given that the resistive force acting on the ship depends on the speed of the ship. Using the axes, sketch a graph to show how the speed v varies with time t after the ship's engines are switched off.

starts at $7.0 / 7.2 \mathrm{~m} \mathrm{~s}^{-1}$ ;
(allow ECF from (d)(i))
correct shape;

Figure for Answer to Question 7 — IB Physics HL

[Maximum number: 2]

A football player kicks a stationary ball of mass 0.45 kg towards a wall. The initial speed of the ball after the kick is $19 \mathrm{~m} \mathrm{~s}^{-1}$ and the ball does not rotate. Air resistance is negligible and there is no wind.

The ball leaves the ground at an angle of $22^{\circ}$ . The horizontal distance from the initial position of the edge of the ball to the wall is 11 m . Calculate the time taken for the ball to reach the wall.

horizontal speed $=19 \times \cos 22$ « $=17.6 \mathrm{~m} \mathrm{~s}^{-1}$ »
$\text { time }=\ll \frac{\text { distance }}{\text { speed }}=\frac{11}{19 \cos 22}=>0.62 \ll \gg$

Marking guidance:

Allow ECF for MP2

[Maximum number: 2]

A football player kicks a stationary ball of mass 0.45 kg towards a wall. The initial speed of the ball after the kick is $19 \mathrm{~m} \mathrm{~s}^{-1}$ and the ball does not rotate. Air resistance is negligible and there is no wind.

In practice, air resistance affects the ball. Outline the effect that air resistance has on the vertical acceleration of the ball. Take the direction of the acceleration due to gravity to be positive.

IB Physics HL A 1 Kinematics Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question 2

Question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (d)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9