Respuesta :
Answer:
w = 0.01 t⁻² rad/h
Explanation:
Let's use trigonometry to find the elevation angle of the telescope, we assume that the rocket remains fixed in the telescope.
tan θ = CO / CA
the adjacent leg is CA = 16 km = 16 10³ m
Let's use kinematics to find the height of the rocket
v = y / t
y = v t
this height is equal to the opposite leg
CO = v t
we substitute
tan θ = vt / 16
tan θ = 1200/16 t
tan θ = 75 t
θ = tan⁻¹ ( 75 t )
speed is defined by
w = dθ/dt
w = [tex]\frac{1}{1 + (75 t)^2} \ 75[/tex]
as time increases we can neglect the 1 of the denominator
w = 1/75 t²
w = 0.0133 t⁻²
Using three significant figures
w = 0.01 t⁻² rad/h
for this answer the time must be given in hours
