Tuesday

July 22, 2014

July 22, 2014

Posted by **Paige** on Tuesday, April 24, 2012 at 11:53pm.

a) How fast is theta decreasing at this instant? express results in units of deg/s

b) How fast is the distance between the aeroplane and the radar station changing at this instant? express the rates in units of ft/s 1 mi = 5280ft

- calculus -
**bobpursley**, Wednesday, April 25, 2012 at 2:24amIf I get the picture accurately

a) height/horizontaldistance away= sinTheta

height= distancaway*sinTheta

take the deriviative

0=d (distance)/dt *sinTheta- distance*cosTheta dTheta/dt

well d (distance)/dt=velocity= 300mi/hr

dTheta/dt= tanTheta*300mi/hr / distance

but distance= height/sin30 then solve for dTheta/dt. Change mi/hr to feet/sec (ie 60mph=88ft/second)

**Related Questions**

calculus - shortly after taking off, a plane is climbing at an angle of 30° and ...

Airplane & Radar - (Airplane & Radar) An airplane is flying (horizontally) at ...

Caculas - (Airplane & Radar) An airplane is flying (horizontally) at the height ...

physics - A plane is found by radar to be flying 5.9 km above the ground. The ...

rate of change - A missile rises vertically from a point on the ground 75,000 ...

Calculus - A plane flying with a constant speed of 4 km/min passes over a ground...

Calculus - A plane flying with a constant speed of 24 km/min passes over a ...

calculus - A plane flying with a constant speed of 23 km/min passes over a ...

CALCULUS - A plane, flying horizontally at an altitude of 1 km and a speed of ...

Calculus - A missile is rising vertically from a point on the ground 75,000 feet...