Question
A road perpendicular to a highway leads to a farmhouse located 6 mile away. An automobile traveling on the highway passes through this intersection at a speed of 55mph.
How fast is the distance between the automobile and the farmhouse increasing when the automobile is 2 miles past the intersection of the highway and the road?
I don't even know where to begin, can someone PLEASE PLEASE PLEASE explain this step by step!
Thank you!!!!
How fast is the distance between the automobile and the farmhouse increasing when the automobile is 2 miles past the intersection of the highway and the road?
I don't even know where to begin, can someone PLEASE PLEASE PLEASE explain this step by step!
Thank you!!!!
Answers
as usual, begin by drawing a diagram. Clearly, the distance z is the hypotenuse of a triangle with sides 2 and 6.
Now, at time t hours from when the car passed the intersection, the distance z is
z^2 = (55t)^2 + 6^2
so, when the car is 2 miles past the intersection, t=2/55, and z=√40
2z dz/dt = 2(55t)(55)
2√40 dz/dt = 2(55 * 2/55)(55)
dz/dt = 17.38 mi/hr
Now, at time t hours from when the car passed the intersection, the distance z is
z^2 = (55t)^2 + 6^2
so, when the car is 2 miles past the intersection, t=2/55, and z=√40
2z dz/dt = 2(55t)(55)
2√40 dz/dt = 2(55 * 2/55)(55)
dz/dt = 17.38 mi/hr