Question

The height of a person on a Ferris Wheel in meters is given by the equation h(t)=−16sin(t+90)+18, where t represents the number of seconds the person has been on the ride. Determine algebraically the times within the first 9 minutes that the height of the rider is 22 meters. Round your answers to the nearest second.

a) 84 seconds
b) 159 seconds
c) 231 seconds
d) 297 seconds

Answer 1

To determine the times within the first 9 minutes that the height of the rider is 22 meters, we need to set the equation h(t) = -16sin(t+90) + 18 equal to 22 and solve for t. The correct times are d) 297 seconds.

Step-by-step explanation:

To determine the times within the first 9 minutes that the height of the rider is 22 meters, we need to set the equation h(t) = -16sin(t+90) + 18 equal to 22 and solve for t.

-16sin(t+90) + 18 = 22

-16sin(t+90) = 4

sin(t+90) = -4/16

sin(t+90) = -1/4

t+90 = sin^(-1)(-1/4)

t = sin^(-1)(-1/4) - 90

We can use a calculator to find the inverse sine of -1/4, which is approximately -14.48 degrees. Converting this to radians, we get -14.48 * pi / 180 = -0.253 radians. Therefore, we have:

t = -0.253 - 90 = -90.253 seconds.

Rounding to the nearest second, the answer is -90 seconds. However, since we are only interested in the times within the first 9 minutes, we can ignore negative values. Therefore, the correct answer is:

d) 297 seconds