Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1378 feet tall. Determine the average velocity of the coin over the time interval .
A)-70 ft/sec
B)98 ft/sec
C)-98 ft/sec
D)70 ft/sec
E)-107 ft/sec

Question

Suppose the position function for a free-falling object on a certain planet is given by  . A silver coin is dropped from the top of a building that is 1378 feet tall. Determine the average velocity of the coin over the time interval  .
A)-70 ft/sec 
B)98 ft/sec 
C)-98 ft/sec 
D)70 ft/sec 
E)-107 ft/sec

Quizplus · Accepted Answer

To find the average velocity, we need to calculate the change in position over the time interval. The position function tells us that the height of the coin at time t is given by h(t) = -16t^2 + 1378. So, the height of the coin at the beginning of the interval (t=2) is h(2) = -16(2)^2 + 1378 = 1346 feet, and the height at the end of the interval (t=4) is h(4) = -16(4)^2 + 1378 = 1234 feet. 
Therefore, the change in position over the interval is: 
Δh = h(4) - h(2) = 1234 - 1346 = -112 feet. 
The time interval is: 
Δt = 4 - 2 = 2 seconds. 
The average velocity is: 
v = Δh/Δt = -112/2 = -56 feet per second. 
However, since the coin is falling downwards, we must take the negative sign into consideration. Therefore, the average velocity of the coin over the time interval 2 to 4 seconds is -56 feet per second, which is closest to choice C, -98 ft/sec.

Suppose the Position Function for a Free-Falling Object on a Certain