After opening the parachute, the descent of a parachutist follows a linear model.At 7:28 P.M., the height of the parachutist is 6150 feet.At 7:31 P.M., the height is 3450 feet.Use a linear equation that gives the height of the parachutist in terms of the time to find the time when the parachutist will reach the ground.
A) 7:33:30 P.M.
B) 7:34:50 P.M.
C) 7:32:00 P.M.
D) 7:37:30 P.M.
E) 7:31:00 P.M.

Question

Quizplus · Accepted Answer

We can use the two given data points to find the slope of the linear equation:

slope = (3450 - 6150) / (3 minutes * 60 seconds/minute) = -900 feet/minute

Next, we can use the point-slope form of the linear equation:

y - y1 = m(x - x1)

where (x1, y1) is one of the data points and m is the slope. Let's use the first data point (7:28 P.M., 6150 feet):

y - 6150 = -900/60 (x - 7*60 - 28)   // convert minutes to seconds

Simplifying the equation, we get:

y = -15x + 7260

To find the time when the parachutist will reach the ground, we need to find the value of x when y = 0 (since height is 0 when the parachutist reaches the ground):

0 = -15x + 7260

x = 484 seconds = 8 minutes and 4 seconds

Therefore, the parachutist will reach the ground at 7:31 P.M. + 8 minutes and 4 seconds = 7:34:50 P.M.

Hence, the answer is B.

After Opening the Parachute, the Descent of a Parachutist Follows