a man is moving away from a 40m high tower at a speed of 2m/sec Find the rate at - Maths - Application of Derivatives

Question

a man is moving away from a 40m high tower at a speed of 2m/sec
Find the rate at which the angle of elevation of the top of the
tower is changing when he is at a distance of 30 meters from the
foot of the tower Assume that the eye level of the man is 1 6m from
the ground

Rishabh Mittal · Accepted Answer

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Given:- dxdt=2 m/sec
Let the angle of elevation=θ
so, tan θ=38 4xθ=tan-138
4xDifferentiating both sides w r
t  't'  dθdt=dtan-138 4xdt=11+38 4x2d38
4xdt        since dtan-1xdx=11+x2        =11+38
4x2-38 4x2dxdt=-38 4 x2x2x2+38
42dxdt      =-38 42x2+38 42=-76
8x2+38 42At x=30 m dθdt=-76 8302+38 42=-76
8900+1474 56=-76 82374 56=-0
032So, angle of elevation is decreasing at the rate 0
032 degree/sec

a man is moving away from a 40m high tower at a speed of 2m/sec .Find the rate at which the angle of elevation of the top of the tower is changing when he is at a distance of 30 meters from the foot of the tower .Assume that the eye level of the man is 1.6m from the ground