contestada

You are looking at the New York ball drop on New year's eve at a distance of 100 m away from the base of the structure. If the ball drops at a constant rate of 2 m/s, what is the rate of change of the angle between you and the ball when the angle is pi/4?

Respuesta :

Answer:

-1/100 radians per second

Step-by-step explanation:

- using tangent of the angle you can solve for y, you should get 100 when you do tan(theta)= y/100 since x also = 100

- then take the derivative of the tangent equation you set up, it should be sec^2(theta)*(rate of change of theta) = (100dy/dt - 0) / y^2

-next plug in the values for dy/dt which is 2 and y which is 100 and theta which is pi/4

-solve for rate of change of theta and answer is -1/100 radians per second