Flugbahnen bestimmen textaufgabe

Question

Kann jemandir Bitte erklärzn wie die Aufgabe geht?

Ich bedanke mich schonmal im Voraus :)

Answer 1

f(x) = TAN(α)·x - 5·x^2/(v·COS(α))^2

a)

f(x) = 0

TAN(α)·x - 5·x^2/(v·COS(α))^2 = 0 -- > x = v^2/5·SIN(α)·COS(α) ∨ x = 0

b)

x(α) = v^2/5·SIN(α)·COS(α)

x'(α) = v^2/5·(2·COS(α)^2 - 1) = 0 --> α = pi/4 = 45°

c)

Sx = v^2/10·SIN(α)·COS(α)

h = f(Sx) = TAN(α)·(v^2/10·SIN(α)·COS(α)) - 5·(v^2/10·SIN(α)·COS(α))^2/(v·COS(α))^2

h = v^2/20·SIN(α)^2