To be able to calculate an object\'s velocity using geometry and calculus. (Figu

Question

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.

Explanation / Answer

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)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.