A stone is tossed into the air from ground level with an initial velocity of 33 meters per second (m/s). Its height at time t is h(t) = 33t − 4.9t2 meters (m)

Question

A stone is tossed into the air from ground level with an initial velocity of 33 meters per second (m/s). Its height at time t is h(t) = 33t − 4.9t² meters (m)

Estimate the instantaneous velocity v at t = 2. Round answer to one decimal place.

v ≈

Answer 1

A stone is tossed into the air from ground level with an initial velocity of 33 meters per second (m/s). Its height at time t is h(t) = 33t − 4.9t² meters (m). Estimate the instantaneous velocity v at t = 2. Round answer to one decimal place. v ≈

Detailed Solution:

Know fact: Derivative of Distance with respect to time h(t) is Velocity v(t): Velocity = d/dt(Distance)

v(t) = d/dt(h(t)) ==> v(t) = d/dt(33t − 4.9t²) ==> v(t) = 33 − 9.8t

v(2) = 33 − 9.8(2) ==> v(2) = 13.4 m/s