A body is dropped from rest and covers 3/4 of the total height during its last 2 s. Find its total time of fall, in second.

Question

G1 Physics · Accepted Answer

Let total time be T. Total height: H = gT²/2. Distance in the last 2 s: s = (g/2)[T²−(T−2)²] = 2g(T−1). Given s/H = 3/4, [4(T−1)]/T² = 3/4. Thus 3T²−16T+16=0. The roots are 4 and 4/3. Since T must exceed 2 s, T=4 s.