Lamp Instant
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A man 2 m tall is watching a street lamp 6 m high as he jogs toward it at a rate of 2m/s.?
How fast is the angle of elevation of the man's line of sight increasing at the instant that he is 3 m from the base of the light?
can someone give me a full solution...i tried this question but didnt get it..thnx very much
how do u get that?
if a is the angle between the line of sight and the horizontal. and x is the horizontal distance using x = 0 when he is level with the lamp therefore our x will be negative. t = time.
the vertical distance between the man and the lamp is 4m
and the horzontal distance is x = vt
tan(a) = 4/x = 4/(vt)
a = atan(4/(vt))
if u = 4/(vt)
du/dt= -4/(vt^2) = -4/(xt)
a = atan(u)
da/du = 1 / (1+u^2) = 1 / (1+ (4/x)^2)
= 1 / (1 + (16/x^2)) = x^2 / (x^2 + 16)
da/dt = da/du*du/dt = -4/(xt) * x^2 / (x^2 +16)
da/dt = -4x / t(x^2 + 16)
It will take him x/v seconds to get there so t = 3/2
so da/dt = -4(-3)/[(3/2)(3^2+16)]
da/dt = 12 / (75 / 2) = 8/25 = 0.32
So the rate of change of the the angle of elevation of the mans line of sight is 0.32rad/s
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