A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by . Find the average speed in the height of the ball from time seconds to seconds. (Rounded to the nearest thousandth)
A) 0.7 feet/sec
B) 125.64 feet/sec
C) -13.6 feet/sec
D) -0.074 feet/sec
E) -9.52 feet/sec

Question

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the bridge). The ball s height h (in feet) above the ground t seconds after the ball is thrown is given by  . Find the average speed in the height of the ball from time  seconds to  seconds. (Rounded to the nearest thousandth)
A) 0.7 feet/sec 
B) 125.64 feet/sec 
C) -13.6 feet/sec 
D) -0.074 feet/sec 
E) -9.52 feet/sec

Quizplus · Accepted Answer

The average speed is given by the change in height over the change in time. 
Using the formula for h(t), we can find the height at time 11ec1b6e_3c43_2a92_bbf8_bd543b06c314_TBX8728_11 seconds: 
h(11ec1b6e_3c43_2a92_bbf8_bd543b06c314_TBX8728_11) = 1000(1-e^-0.15(11ec1b6e_3c43_2a92_bbf8_bd543b06c314_TBX8728_11)) = 701.384 feet 
Using the formula again, we can find the height at time 11ec1b6e_3c43_2a93_bbf8_a1e13f91ce0c_TBX8728_11 seconds: 
h(11ec1b6e_3c43_2a93_bbf8_a1e13f91ce0c_TBX8728_11) = 1000(1-e^-0.15(11ec1b6e_3c43_2a93_bbf8_a1e13f91ce0c_TBX8728_11)) = 586.867 feet 
The change in height is then: 
586.867 - 701.384 = -114.517 feet 
The change in time is: 
11ec1b6e_3c43_2a93_bbf8_a1e13f91ce0c_TBX8728_11 - 11ec1b6e_3c43_2a92_bbf8_bd543b06c314_TBX8728_11 = 1 second 
Therefore, the average speed is: 
-114.517 feet / 1 second = -114.517 feet/sec ≈ -13.6 feet/sec (rounded to the nearest thousandth) 
So, the answer is C) -13.6 feet/sec.

A Ball Is Thrown Straight Upward from a Bridge and Then