maximum height of 100 meters and a diameter of 50 meters. It takes the wheel seven minutes to make one revolution.counter clockwise how many seconds will it take for your seat to reach a height of 75 meters? Round

Assuming the wheel goes
counter-clockwise, and at t=0 min the chair is at ground, or f(0)=0.

Then
at t minute, the wheel goes up 360 x t/7 degree.

So
the height f(t)=50-50cos(360t/7)

When
f(t)=75 meters, 75=50-50cos(360t/7), cos(360t/7)=-25/50=-0.5

So
360t/7=120 or 360t/7=240

t=7/3min=7/3x60 seconds=140 seconds

or
t=7x2/3 min=7x2/3x60 seconds=280 seconds

Therefore it will take either 140 seconds or 280 seconds to reach the height of 75 meters. This is reasonable since the wheel moves in a round trajectory, so it will be at the same height twice excluding the highest and the lowest points.