Thread: Related rates question.

1. Related rates question.

I got 356.84 km/hr for the question below, do you think this is correct?

A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later?

Here is my work:

dx/dt=360

y^2=x^2+3^2-2(3)(x)cos120degrees
=x^2+9-6x(-1/2)
=x^2+3x+9

2y dy/dt= 2x dx/dt + dx/dt
dy/dt= (2x+1)/2y dx/dt

dy/dt= (13/2y) *360

x= 360/60= 6 km

dy/dt= 2(6)+ 3/2 sqrt 43 *360
= (13/2sqrt 43) *360= 356.84 km/hr

2. Originally Posted by ioke09
I got 356.84 km/hr for the question below, do you think this is correct?

A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later?

Here is my work:

dx/dt=360

y^2=x^2+3^2-2(3)(x)cos120degrees
=x^2+9-6x(-1/2)
=x^2+3x+9

2y dy/dt= 2x dx/dt + dx/dt<--- 2y dy/dt= 2x dx/dt + 3 dx/dt
dy/dt= (2x+1)/2y dx/dt

dy/dt= (13/2y) *360

x= 360/60= 6 km

dy/dt= 2(6)+ 3/2 sqrt 43 *360
= (13/2sqrt 43) *360= 356.84 km/hr
Just a small mistake in taking the derivative otherwise you are doing it correctly.