Shadow Dynamics with Varying Velocity

[dan_and_sim]

Homework Statement

A small light source is located a distance L from a vertical wall. An object
of height h moves with constant velocity v towards the wall, causing a shadow
on the wall. At time t = 0 the object is located at the source S.

(a) Compute the height of the shadow, D, as a function of time.
(b) Compute the velocity, u, and the acceleration, a, of the shadow’s top.
(c) Consider now the case where the height of the object is not constant,
but varies with time according to
h(t) = h0 + b cos(w t)
with h0, b and w constant. Compute the velocity u and the acceleration
a of the shadow’s top.
(d) Sadly, the velocity of the object now also depends on time,
v(t) = v0 e^−t/t0
With h(t) as given in (c), compute u.

 

[jbsteele]

Homework Equations Not sure.The Attempt at a Solution (a) The height of the shadow, D, as a function of time is D = h-L/v*t.(b) The velocity, u, and the acceleration, a, of the shadow's top are u = -L/v*t and a = -L/v.(c) The velocity, u, and the acceleration, a, of the shadow's top are u = -L/(v0+b*w*sin(wt)) and a = -L/(v0+b*w*sin(wt))^2.(d) The velocity, u, of the shadow's top is u = -L/(v0*e^(-t/t0)+b*w*sin(wt)).