Assume an object weighing 7 pounds is dropped from a height of 9,000 feet, where the air resistance is proportional to the velocity. Round numerical answers in your answer to two Places.
(i) Write the velocity as a function of time if the object's velocity after 6 seconds is 3.50 feet per
Second.
(ii) What is the limiting value of the velocity function?
A)
(i) $v ( t ) = 3.5000 \left( 1 - e ^ { - 9.1429 t } \right)$;
(ii) 0
B) (i) $v ( t ) = 3.5000 \left( 1 - e ^ { 9.1429 t } \right)$;
(ii) 0
C) (i) $v ( t ) = 3.5000 \left( 1 - e ^ { - 9.1429 t } \right)$;
(ii) $3.5000$
D) (i) $v ( t ) = 3.5000 \left( 1 - e ^ { 9.1429 t } \right)$;
(ii) $3.5000$
E) (i) $v ( t ) = 3.5000 \left( 1 + e ^ { 9.1429 t } \right)$;
(ii) limit does not exist

Question

Assume an object weighing 7 pounds is dropped from a height of 9,000 feet, where the air resistance is proportional to the velocity. Round numerical answers in your answer to two Places.
(i) Write the velocity as a function of time if the object's velocity after 6 seconds is 3.50 feet per
Second.
(ii) What is the limiting value of the velocity function? 
A)
(i) $v ( t ) = 3.5000 \left( 1 - e ^ { - 9.1429 t } \right)$;
(ii) 0
B) (i) $v ( t ) = 3.5000 \left( 1 - e ^ { 9.1429 t } \right)$;
(ii) 0
C) (i) $v ( t ) = 3.5000 \left( 1 - e ^ { - 9.1429 t } \right)$;
(ii) $3.5000$
D) (i) $v ( t ) = 3.5000 \left( 1 - e ^ { 9.1429 t } \right)$;
(ii) $3.5000$
E) (i) $v ( t ) = 3.5000 \left( 1 + e ^ { 9.1429 t } \right)$;
(ii) limit does not exist

Quizplus · Accepted Answer

The velocity function for an object with air resistance proportional to velocity is typically of the form $v(t) = v_{\text{terminal}}(1 - e^{-kt})$. Given that the velocity after 6 seconds is 3.50 feet per second, choice A correctly represents this form. The limiting value of the velocity function as $t$ approaches infinity is 0, as the object will eventually stop accelerating due to air resistance.

Assume an Object Weighing 7 Pounds Is Dropped from a Height