PROBLEM
Siraj and Son Live near eachother. Sirajs house is 20 km east of Sons house. Siraj runs 12 km/h to sons house. son goes south to the beach at 9km/h. they start
Siraj and Son Live near eachother. Sirajs house is 20 km east of Sons house. Siraj runs 12 km/h to sons house. son goes south to the beach at 9km/h. they start at 9 and go on for 2.5 hours. when will they be closest to eahother
Siraj and Son Live near eachother. Sirajs house is 20 km east of Sons house. Siraj runs 12 km/h to sons house. son goes south to the beach at 9km/h. they start at 9 and go on for 2.5 hours. when will they be closest to eahother
SOLUTION
Let's look at the distance between Siraj and Son as a function of time.
The x distance between them is: 20 - 12t
The y distance between them is: 9t
Using the Pythagorean Theorem, the distance between them at any point in time can be found using: d2 = x2 + y2
Therefore, d2 = (20 - 12t)2 + (9t)2
d2 = 400 - 480t + 144t2 + 81t2
d2 = 144t2 + 81t2 - 480t + 400
d2 = 225t2 - 480t + 400
To find the minimum distance, take the derivative of the above equation and set it equal to zero and solve for t.
(d/dt)[d2]= (d/dt)[225t2 - 480t + 400]
0 = 450t - 480
450t = 480
t = 480/450
t ≈ 1.0666666 hrs
Therefore, Siraj and Son are closest after approximately 1.067 hrs.
