State the significance of the negative values of s.

Use the graph to

(i) estimate the velocity of the ball at t \( = \) 0.80 s.

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

The following data are available.

Mass of the ball = 0.20 kg

Mean radius of the Moon = 1.74 \( \times \) 10⁶ m

Mean orbital radius of the Moon about the centre of Earth = 3.84 \( \times \) 10⁸ m

Mass of Earth = 5.97 \( \times \) 10²⁴ kg

Show that Earth has no significant effect on the acceleration of the ball.

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

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.)

Explain, in terms of the number of nucleons and the forces between them, why calcium-40 is stable and calcium-47 is radioactive.

Calculate the percentage of a sample of calcium-47 that decays in 27 days.

The nuclear equation for the decay of calcium-47 into scandium-47 \(\left( {{}_{21}^{47}{\rm{Sc}}} \right)\) is given by

\[{}_{20}^{47}{\rm{Ca}} \to {}_{21}^{47}{\rm{Sc + }}{}_{ - 1}^0{\rm{e + X}}\]

(i) Identify X.

(ii) The following data are available.

Mass of calcium-47 nucleus = 46.95455 u
Mass of scandium-47 nucleus = 46.95241 u

Using the data, determine the maximum kinetic energy, in MeV, of the products in the decay of calcium-47.

(iii) State why the kinetic energy will be less than your value in (h)(ii).

upwards (or away from the Moon) is taken as positive / downwards (or towards the Moon) is taken as negative / towards the Earth is positive;

7.7 m s\(^{ - 1}\);

curve permanently below Moon curve;

smooth parabola; (judge by eye)

line passing through s = −3.00 m, t = 0.78 s or s = −3.50 m, t = 0.84 s (±1mm);