A person is walking towards a wall at a constant speed of 9 km/h. At the top of the 30 meters wall is a bilboard. At what speed is the person approaching the base of the bilboard(top of the wall) when he is at 40 m from the wall ?
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If the person is a distance x from the base of a wall with height h, then they are a distance
s = √[ x² + h² ]
from the top of the wall. The time rate of change of s will be the speed with which they approach the top of the wall. Take the time derivative of s, and don't forget the chain rule.
ds/dt = { (½) / √[ x² + h² ] } 2x dx/dt
ds/dt = ( x dx/dt ) / √[ x² + h² ]
Note that 9 km/hr is 2.5 m/s
ds/dt = (40 m)(2.5 m/s) / √[ (40 m)² + (30 m)² ] = 2.0 m/s
s = √[ x² + h² ]
from the top of the wall. The time rate of change of s will be the speed with which they approach the top of the wall. Take the time derivative of s, and don't forget the chain rule.
ds/dt = { (½) / √[ x² + h² ] } 2x dx/dt
ds/dt = ( x dx/dt ) / √[ x² + h² ]
Note that 9 km/hr is 2.5 m/s
ds/dt = (40 m)(2.5 m/s) / √[ (40 m)² + (30 m)² ] = 2.0 m/s
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9 km/h
Assuming your premise holds.
Assuming your premise holds.
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7.1km/h
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9km/h
Because you said he was walking at a constant speed. I doubt he will suddenly slow down or speed up...
Because you said he was walking at a constant speed. I doubt he will suddenly slow down or speed up...