To be able to calculate an objects velocity using geometry a

To be able to calculate an object\'s velocity using geometry and calculus. (Figure 1) A light source, S, is located at a distance l from a wall. An opaque object of height h moves toward the wall with a constant velocity v. At time t = 0, the object is located at the source S. Expression for the magnitude of velocity of shadow. Find an expression for v_s, the magnitude of the velocity v_s, of the top of the object\'s shadow, at time t. Express the speed of the top of the object\'s shadow in terms of t, v, l, and h.

Solution

This problem can be done with ratios.

there are two right triangles. One is formed by V*t and h .

v*t is the dstance the wall traveled from s. and \' h\' is the height of wall. this form a ratio :

ratio = h /(v*t)

now there is the second triangle , which is formed by I and Vs *t which is the distance the shadow traveled. this has same ratio as first triangle.

ratio 2 = Vs * t / l

since the ratios are equal we place them in an equation and solve for Vs

ratio = ratio 2

h/ v*t = vs * t / l

solve for Vs

Vs = (h* l) /( v* t²)