

Explanation
(a) From a displacement - time graph, the following can be deduced
(i) Uniform velocity
(ii) Instantaneous velocity
(iii) Initial displacement

(b) The force would remain the same Gram =
\(F_2 = \frac{Gmm}{r^2}\)
F\(_2\) = \(\frac{G2m \times 2m}{(2r)^2}\)
=\(\frac{G4m^2}{4r^2}\)
= \(\frac{Gm^2}{r^2}\)
= \(\frac{Gmm}{r^2}\)
\(F_1 = F_2\)

(c)Factors that affect maximum height of a bullet include
(i) Initial velocity / speed
(ii) Acceleration due to gravity
(iii) Angle of projection
(iv) Air resistance

(d)Practical examples of mechanical resonance include:
(i) Shattering of glass due to high pitch note.
(ii) Throwing of 2 paper rider from a vibrating stretched string
(iii) Collapse of a bridge by matching soldiers
(iv) Car bodies rattle (at very high speed)

(e)

acceleration = g sin \(\theta\) – \(\mu\) cos \(\theta\)
a =10 x sin 30 – 0.3 x 10 x cos30
=10 x 0.5 –0.3 x 10 x 0.8660
= 5 – 2.598
= 2.4m/s\(^2\)
Distance covered, s = \(\frac{4}{\sin30}\)
= \(\frac{4}{0.5}\)
= 8m
Using S = Ut + \(\frac{1}{2}\)at\(^2\)
8 =\(\frac{1}{2}\) x 2.4 x r\(^2\)
8 = 1.2\(t^2\)
\(r^2\) = \(\frac{8}{1.2}\)
= 2.58s

