two cars p and a are moving at uniform speeds 50 km per hour and 25 km per hour on two straight roads intersecting at right angles to each other.p passes the intersection point while q is 50 km away from intersection point.what is the shortest distance between the cars during journey
Answers
two cars p and a are moving at uniform speeds 50 kmh and 25 kmh perpendicularly the shortest distance between them = 44.72 km
Step-by-step explanation:
Two cars p and a are moving at uniform speeds 50 km per hour and 25 km per hour on two straight roads intersecting at right angles to each other
Let say intersection point is O
Distance of q from O = 50 km when Distance of p from O = 0 km
Distance between p & q = √op² + oq² = 50 km
Let say T Hrs After Distances
OP = 0 + 50T
OQ = 50 - 25T
Distance² = OP² + OQ² = (50T)² + (50 - 25T)²
= 25² ( 4T² + ( 2 - T)²)
= 25² ( 4T² + 4 + T² - 4T)
= 25² ( 5T² - 4T + 4)
Differentiating with T and putting = 0
10 T - 4 = 0
=> T = 4/10
After 4/10 hrs Distance will be minimum
Putting T = 4/10 in above equation
Distance² = 2000
=> Distance = √ 2000 = 44.72 km
Distance of p = 50 ( 4/10) = 20 km
Distance of q = 50 - 25(4/10) = 40 km
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