A skydiver moving vertically experiences an acceleration (in meters per second…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A skydiver moving vertically experiences an acceleration (in meters per second squared) modeled by a(t)=9.8−0.2t for 0≤t≤10, where t is measured in seconds. At the instant the skydiver exits the aircraft (t=0), her velocity is 0m/s and her altitude above the ground is 1200 meters.
(a) Integrate a(t) to obtain a general expression for the velocity v(t), including the appropriate constant of integration.
(b) Use the given information to determine the particular velocity function valid for 0≤t≤10. Show all algebraic steps.
(c) Integrate your result from part (b) to derive a general formula for altitude h(t) (in meters) above the ground. Include any new constant of integration that appears.
(d) Apply the initial altitude to obtain the specific altitude function for the skydiver. Then calculate her altitude at t=10 seconds. Express your answer to the nearest meter and interpret its significance with respect to the impending deployment of a parachute.