A girl of height 120 cm is walking towards a light on the ground at a speed of 0.6 m/s. Her shadow is being cast on a wall behind her that is 5 m from the light.
How is the size of her shadow changing when she is 1.5 m from the light?
draw a diagram. Using similar triangles, if her shadow has height h when she is x cm from the light, then
h/500 = 120/x
or,
hx = 60000
so,
h dx/dt + x dh/dt = 0
Now, find h when x = 150, and you know that dx/dt = -60 cm/s; you can then find dh/dt
To understand how the size of the girl's shadow is changing, we need to consider the concept of similar triangles.
First, let's draw a diagram to visualize the situation. The light source is on the ground, and the girl's shadow is cast on a wall located 5 m away from the light. We can assume that the light is directly above the girl's head, so her height of 120 cm is the length of her shadow when she is standing at the starting position.
Now, let's calculate the length of her shadow when she is 1.5 m away from the light. To do this, we'll use the concept that similar triangles have proportional sides.
We can set up a proportion using the lengths of the girl's shadow and her distance from the light at two different positions.
When she is at the starting position:
120 cm (height of girl) / 5 m (distance from light to wall) = x (length of shadow when she is 1.5 m away from the light) / 1.5 m (distance from light to girl's current position)
To find the length of her shadow at the new position, we need to solve for x.
Let's solve the proportion using cross-multiplication:
120 cm * 1.5 m = 5 m * x
180 cm*m = 5 m * x
180 cm*m / 5 m = x
36 cm = x
Therefore, when the girl is 1.5 m away from the light, her shadow will be 36 cm long.