Question

A stone is thrown from a rooftop at time t = 0 seconds. Its position at time t is given by r(t)=8t i -5t j +(14.7-4.9t^2)k . The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north and k points up.

How high is the rooftop?

Answer 1

The rooftop's height is determined using the initial condition of the stone's vertical position at t = 0 seconds, which is indicated by the k component of the position vector and is 14.7 meters.

Step-by-step explanation:

The height of the rooftop can be determined from the initial conditions of the stone's position. At time t = 0 seconds, the stone is thrown from the rooftop and its position vector r(t) is given as r(t) = 8t i - 5t j + (14.7 - 4.9t^2) k. The k component of the position vector (which points upwards) represents the vertical motion of the stone. The initial height of the rooftop is given by the coefficient of the k component at t = 0, which is 14.7 meters. Therefore, the rooftop is 14.7 meters high.