1. An airplane has a speed of 600 km h−1 with respect to air. It has to fly a distance of 800 km
northward. In what direction should it fly if a steady wind is blowing at a speed of
120 km h−1 from the west? What will its speed with respect to the ground be? Draw the
relevant diagram for your calculations.
2. A plane is flying with a constant speed along a straight line at an angle of 60° with the
horizontal. The weight W of the plane is 90, 000 N and its engine provides a thrust T of
120, 000 N in the direction of flight. Two additional forces are exerted on the plane: the lift
force F perpendicular to the plane’s wings, and the force R due to air resistance opposite to
the direction of motion. Draw the free-body diagram showing all forces on the plane.
Determine F and R.
3. A bus is moving downhill at a slope of 5°. At the moment when the speed of the bus is
30 km h−1, the driver spots a deer 30m ahead. He applies the brakes and comes to a stop.
The deer is paralyzed by fear and does not move. Will the bus stop before reaching it or
will it hit the deer? Do relevant calculations and draw appropriate force diagram. Take the
coefficient of kinetic friction to be μk = 0.26.
4. A circular disc rotates on a thin air film with a period of 0.3s. Its moment of inertia about its
axis of rotation is 0.06 kg m2. A small mass is dropped onto the disc and rotates with it. The
moment of inertia of the mass about the axis of rotation is 0.04 kg m2. Determine the final
period of the rotating disc and mass.
5. Obtain an expression for the time period of a satellite orbiting the earth. At what altitude
should a satellite be placed for its orbit to be geosynchronous?
6. At perihelion on Feb. 9, 1986, Halley’s comet was 8.79 × 107 km from the sun and was
moving at a speed of 54.6 km s−1 relative to the sun. Calculate its speed (a) when the comet
was 1.16 × 108 km from the sun, and (b) at its next aphelion in the year 2024, when the
comet will be 5.28 × 109 km from the sun.
7. An object was launched with a velocity of 20 ms−1 at an angle of 45° to the vertical. At the
top of its trajectory the object broke into two equal pieces. One piece fell vertically
downwards. Where would the other piece fall? (Take g = 10 ms−2)
8. Show that for Rutherford scattering, twice as many particles are scattered through an angle
between 60° to 90° as are scattered through angles of 90° or more.
9. An ice skater spins about a vertical axis at an angular speed of 15 rad s−1 when her arms are
outstretched. She then quickly pulls her arms into her sides in a very small time interval so
that the frictional forces due to ice are negligible. Her initial moment of inertia about the
axis of rotation is 1.72 kg m2 and her final moment of inertia is 0.61 kg m2. What is the
change in her angular speed? What is the change in her kinetic energy? Explain this change
in kinetic energy.
4
10. a) Calculate the Coriolis acceleration of an aeroplane flying along the equator due east at
a speed of 300m s−1.
b) Explain why the following statement is wrong:
‘The moon does not fall down as it moves around the earth because the centrifugal
force balances the force of gravitation and hence there is no net force to make it fall.’
1. An airplane has a speed of 600 km h−1 with respect to air. It has to fly a distance of 800 km
northward. In what direction should it fly if a steady wind is blowing at a speed of
120 km h−1 from the west? What will its speed with respect to the ground be? Draw the
relevant diagram for your calculations.
2. A plane is flying with a constant speed along a straight line at an angle of 60° with the
horizontal. The weight W of the plane is 90, 000 N and its engine provides a thrust T of
120, 000 N in the direction of flight. Two additional forces are exerted on the plane: the lift
force F perpendicular to the plane’s wings, and the force R due to air resistance opposite to
the direction of motion. Draw the free-body diagram showing all forces on the plane.
Determine F and R.
3. A bus is moving downhill at a slope of 5°. At the moment when the speed of the bus is
30 km h−1, the driver spots a deer 30m ahead. He applies the brakes and comes to a stop.
The deer is paralyzed by fear and does not move. Will the bus stop before reaching it or
will it hit the deer? Do relevant calculations and draw appropriate force diagram. Take the
coefficient of kinetic friction to be μk = 0.26.
4. A circular disc rotates on a thin air film with a period of 0.3s. Its moment of inertia about its
axis of rotation is 0.06 kg m2. A small mass is dropped onto the disc and rotates with it. The
moment of inertia of the mass about the axis of rotation is 0.04 kg m2. Determine the final
period of the rotating disc and mass.
5. Obtain an expression for the time period of a satellite orbiting the earth. At what altitude
should a satellite be placed for its orbit to be geosynchronous?
6. At perihelion on Feb. 9, 1986, Halley’s comet was 8.79 × 107 km from the sun and was
moving at a speed of 54.6 km s−1 relative to the sun. Calculate its speed (a) when the comet
was 1.16 × 108 km from the sun, and (b) at its next aphelion in the year 2024, when the
comet will be 5.28 × 109 km from the sun.
7. An object was launched with a velocity of 20 ms−1 at an angle of 45° to the vertical. At the
top of its trajectory the object broke into two equal pieces. One piece fell vertically
downwards. Where would the other piece fall? (Take g = 10 ms−2)
8. Show that for Rutherford scattering, twice as many particles are scattered through an angle
between 60° to 90° as are scattered through angles of 90° or more.
9. An ice skater spins about a vertical axis at an angular speed of 15 rad s−1 when her arms are
outstretched. She then quickly pulls her arms into her sides in a very small time interval so
that the frictional forces due to ice are negligible. Her initial moment of inertia about the
axis of rotation is 1.72 kg m2 and her final moment of inertia is 0.61 kg m2. What is the
change in her angular speed? What is the change in her kinetic energy? Explain this change
in kinetic energy.
4
10. a) Calculate the Coriolis acceleration of an aeroplane flying along the equator due east at
a speed of 300m s−1.
b) Explain why the following statement is wrong:
‘The moon does not fall down as it moves around the earth because the centrifugal
force balances the force of gravitation and hence there is no net force to make it fall.’
