Mark the correct alternative in the following: A man of height 6 ft walks at a uniform speed of 9 ft/sec from a lamp fixed at 15 ft height. The length of his shadow is increasing at the rate of

Question

Philoid · Accepted Answer

Given that h_m=6ft, h_l=15ft, v_m=9ft/sec. We have to calculate v_s (speed of shadow).

After time t secs, the man would have moved distance 9t ft away from the lamp. Let the shadow move a distance of x ft in time t secs.

Consider ∆AEC and ∆BED

∠AED=∠BED=θ (common angle)

∠EAC=∠EBD=90°

Therefore, ∆AEC~∆BED by AA criteria

Substituting values, we get

Simplifying the equation, we get

x=6t – (1)

Differentiating (1) with respect to t, we get

Mark the correct alternative in the following:A man of height 6 ft walks at a uniform speed of 9 ft/sec from a lamp fixed at 15 ft height. The length of his shadow is increasing at the rate of

Mark the correct alternative in the following:
A man of height 6 ft walks at a uniform speed of 9 ft/sec from a lamp fixed at 15 ft height. The length of his shadow is increasing at the rate of