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recoil33
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"Differential Approximation"
A person of height 1.9m is walking away from a lamp-post at 1m/s. The light on the lamp-post is 5.1m above the ground.
1. At what rate (in m/s to the nearest cm/s) is the length of the person's shadow changing?
2. At what speed (in m/s to the nearest cm/s) is the tip of the person's shadow moving across the ground?
Alright, I'll be one second to type my working out. I really do not understand what I'm doing much. Any help would be appreciated.
1.9/s = 5.1/s+x
ds/dt + dx/dt
1.9/s = 5.1/(s+x) ---> 1.9(s+x)=13s
1.9(ds/dt + dx/dt) = 13(ds/dt)
we know that dx/dt = 1 ms^-1 (the speed he's walking)
therefore.
s' + x' = (1.9*1)/(5.1-1.9) + 1 = 4.8/3.2
therefore, i got the shadow moving at 4.8/3.2 m/s which is wrong? ;s
A person of height 1.9m is walking away from a lamp-post at 1m/s. The light on the lamp-post is 5.1m above the ground.
1. At what rate (in m/s to the nearest cm/s) is the length of the person's shadow changing?
2. At what speed (in m/s to the nearest cm/s) is the tip of the person's shadow moving across the ground?
Alright, I'll be one second to type my working out. I really do not understand what I'm doing much. Any help would be appreciated.
1.9/s = 5.1/s+x
ds/dt + dx/dt
1.9/s = 5.1/(s+x) ---> 1.9(s+x)=13s
1.9(ds/dt + dx/dt) = 13(ds/dt)
we know that dx/dt = 1 ms^-1 (the speed he's walking)
therefore.
s' + x' = (1.9*1)/(5.1-1.9) + 1 = 4.8/3.2
therefore, i got the shadow moving at 4.8/3.2 m/s which is wrong? ;s
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