During a cycle race, two persons A & B moving with velocity 16 m/s & 12 m/s respectively.
At t=0, B observes A, 10 m ahead of him, in order to win the race they start accelerating
at 1 m/s2 and 2 m/s respectively. Unfortunately both finish simultaneously. The time
(in sec) at which they finish the race is euqalto (t = 10 k), then value of k is :
Answers
Given : During a cycle race, two persons A & B moving with velocity 16 m/s & 12 m/s respectively. At t=0, B observes A, 10 m ahead of him, in order to win the race they start accelerating at 1 m/s2 and 2 m/s respectively.
both finish simultaneously in time = 10k secs
To Find : value of k
Solution:
A Velocity = 16 m/s
acceleration = 1 m/s²
B Velocity = 12 m/s
acceleration = 2 m/s²
B observes A, 10 m ahead of him
=> Distance covered by B = Distance covered by A + 10
time = 10 k
S = ut + (1/2)at²
=> 12*10k + (1/2)(2)(10k)² = 16*10k + (1/2)(1)(10k)² + 10
=> 120k + 100k² = 160k + 50k² + 10
=> 50k² -40k - 10 = 0
=> 5k² -4k - 1 = 0
=> 5k² -5k + 1k - 1 = 0
=> 5k(k - 1) + 1(k - 1) = 0
=> (5k + 1)(k - 1) = 0
=> k = 1
value of k = 1
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Answer:
use 2nd and 3rd equation of motion