Asked by Katie
Two trucks start from the same point. One truck travels due east at a rate of 50 mph and the other trucks travels due north at a rate of 60 mph. At what rate is the distance between the two vehicles increasing 1 1/2 hours later?
I think the answer is 55 mph because I added 60 + 55 and divided by 2 and got 55 mph.
I think the answer is 55 mph because I added 60 + 55 and divided by 2 and got 55 mph.
Answers
Answered by
Damon
Oh my :(
The distance between them is the hypotenuse of a right triangle.
D^2 = x^2 + y^2
where
x = 50 t
y = 60 t
so
D^2 = 2500 t^2 + 3600 t^2 = 6100 t^2
now take time derivative
2 D dD/dt = 12200 t
at t = 1.5
D^2 = 6100 (2.25)
D = 117 miles
2 D = 234.3 miles
so
dD/dt = 12200(1.5)/234.3 = 78.1 miles/hour
The distance between them is the hypotenuse of a right triangle.
D^2 = x^2 + y^2
where
x = 50 t
y = 60 t
so
D^2 = 2500 t^2 + 3600 t^2 = 6100 t^2
now take time derivative
2 D dD/dt = 12200 t
at t = 1.5
D^2 = 6100 (2.25)
D = 117 miles
2 D = 234.3 miles
so
dD/dt = 12200(1.5)/234.3 = 78.1 miles/hour
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.