A light shines frm the top of a pole 50ft high.A ball is dropped frm the same height frm a point 30ft away frm the light.How fast is the shadow of the ball moving along the ground 1/2sec later?(Assume the ball falls s=16t^2ft in t sec)
A light shines frm the top of a pole 50ft high.A ball is dropped frm the same height frm a point 30ft away frm the light.How fast is the shadow of the ball moving along the ground 1/2sec later?(Assume the ball falls s=16t^2ft in t sec)
hello,
I've attached a drawing of the situation.
You are dealing with 2 similar triangles. You can set up the proportion:
. Solve for y because that's the length which the shadow of the ball is away from the pole:
. You are told that . Substitute the variable s and you'll get the equation:
You know that speed is the first derivative wrt t of the length:
The speed at is: