Asked by Arsh 2
Two cars are moving with a constant speed towards finish marker, car A is moving from the north at 16km/hr and car B is moving rom east, when equidistant from the marker the cars are 18km apart and distance between them is decreasing at rate of 19km/hr. Which car Will win the race.?
Answers
Answered by
oobleck
Setting t=0 at the given moment, if both cars had the same speed (16 km/hr), then
z^2 = 2(18/√2 - 16t)^2
z dz/dt = 2(18/√2 - 16t)(-16)
At t=0, that would mean that
18 dz/dt = 2(18/√2)(-16)
dz/dt = -32/√2 = -22.6 km/hr
But, we know that dz/dt = -19 km/hr. That is, it is decreasing more slowly than it would if B were going at 16 km/hr. So, B is moving more slowly than A.
A will win the race.
z^2 = 2(18/√2 - 16t)^2
z dz/dt = 2(18/√2 - 16t)(-16)
At t=0, that would mean that
18 dz/dt = 2(18/√2)(-16)
dz/dt = -32/√2 = -22.6 km/hr
But, we know that dz/dt = -19 km/hr. That is, it is decreasing more slowly than it would if B were going at 16 km/hr. So, B is moving more slowly than A.
A will win the race.
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