I agree. It should be but when I downloaded his solutions yesterday they said that answer not the incorrect one mentioned above. I assume he corrected his answers in response to your post?
Anyway his answer for Q5(c)(iii) I think is wrong. Aren't we integrating with respect to h from -b to b...
I agree with the above answer given. Just apply the sum of a GP formula separately 2 each of the two GP's then add sums 2gether.
ie. G1: a = 2*3^1 = 6 , r = 3
G2: a = 3*2^1 = 6, r = 2
Here's how to do Q2
Let V = projected initial velocity, @ = projected initial angle
Therefore Vy (vertical velocity component) = Vsin@
Therefore Vx (horizontal velocity component) = Vcos@
Derive the following two standard results to begin with:
(1) Max Height Reached (b) =...
Your answer is correct but your method leaves a bit to be desired.
Just as with limits with polynomials divide numerator/denominator through by the term with the highest power and then apply the basic rule that lim (x->infinity) [1/x] = 0
[5(10^n)+3]/(10^n)
-------------------------...
Here is a method that does use calculus (integration & constant)
(a)
dV/dt = K (K<0 since the volume constantly decreases over time)
Integrating with respect to t
V = Kt + C
x^3 = Kt + C
When t=0 x=10 => C=1000
x^3 = 1000 + Kt
When t=70 x=5
125 = 1000 + 70K
70K = -875
K = -12.5 m/s...
x = t2 - 5t - 4 (t>=0)
v = 2t - 5
a = 2
Change in direction will only occur when v=0 and a<>0
0 = 2t - 5
t = 2.5 => x = -2.25
When t=0 x=4 and when t=4 x=0
[--->----]
[---<---------------<----]
|---------0--------------4--------------------->x
-2.25...
Mmm.. rather than use "tricks" such as 3 = e^(ln3) I would go for the straightforward option using indice laws then solving equation
e^(2x) = 3e^(-x)
e^(2x) = 3 / e^x
e^(2x + x) = 3
e^(3x) = 3
3x = ln 3
x = (ln3)/3