Question

You're a consultant on a movie set, and the producer wants a car to drop so that it crosses the camera's field of view in time t. The field of view has height h. Derive an expression for the height above the top of the field of view from which the car should be released.Express your answer in terms of the variables h, t, and appropriate constants.

Answer 1

Given:

You're a consultant on a movie set, and the producer wants a car to drop so that it crosses the camera's field of view in time t. The field of view has height h. Derive an expression for the height above the top of the field of view from which the car should be released.Express your answer in terms of the variables h, t, and appropriate constants.

The differential equation governing   as a funtion of time is :

   with initial conditions    and     .

We can integrate both sides of with respect to time :

  ===> Use initial condition :

===>   . We thus have the velocity equation :

   . Integrate both sides again with respect to time , and we get :

  . Now , use initial condition   :

===>   .

We thus have the equation for is :

   . The car drops units when in :

===>

   --- SOLUTION .