The height (h) of the water in metres at a certain point at the wave pool over a period of seconds is modelled by the equation #h(s)=sin^2s+1/2sins+3/2#?
How high is the water after 2 seconds?
During the first 10 seconds, how many times does the wave height reach 3 metres?
During the first 5 seconds, at what 3 points is the water level at 2 metres?
How high is the water after 2 seconds?
During the first 10 seconds, how many times does the wave height reach 3 metres?
During the first 5 seconds, at what 3 points is the water level at 2 metres?
1 Answer
Simply find the value of
#h(2) = sin^2(2) + 1/2sin(2) + 3/2#
#h(2) = 2.78# meters
For the second part, we must solve for when
#3 = sin^2s + 1/2sins + 3/2#
#0 = sin^2s + 1/2sins - 3/2#
#0 = 2sin^2s + sins - 3#
#0 = 2sin^2s - 2sins + 3sins - 3#
#0 = 2sins(sins - 1) + 3(sins - 1)#
#0 = (2sins + 3)(sins - 1)#
#sins = -3/2 or sins = 1#
Since
For the final part, we must set
#2 = sin^2s + 1/2sins + 3/2#
#0 = sin^2s + 1/2sins - 1/2#
#0 = 2sin^2s + sins - 1#
#0 = 2sin^2s + 2sins - sins - 1#
#0 = 2sins(sins + 1) - (sins + 1)#
#0 = (2sins - 1)(sins + 1)#
#sins = 1/2 and sins = -1#
Since
#s = pi/6, (5pi)/6, (3pi)/2#
Thus
#s ~~0.52 s, 2.62 s, 4.71 s#
Hopefully this helps!