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A plane flying with a constant speed of 29 \(\frac{km}{min} \) passes over a ground radar station at an altitude of 7 km and climbs at an angle of 40 degrees. What is the distance between the radar station and the plane after 4 minutes? At what rate is the distance from the plane to the radar station increasing 4 minutes later?

 Apr 4, 2022
 #1
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x distance from the station =    s * t  cos 40                    s = speed  ( in km/min)       t = time (in miutes)

y distance from the station =    7 + s*t sin 40

 

 

Using distance formula :

  d2 = (s t cos 40)2 + (7 + s t sin 40 )2             Given:     s t = 29 * 4 = 116    <===== subst. in and solve for d

 

Take the derivative with respect to 't'  to find out how fast it is changing at t= 4     <====== can you do that?

 Apr 4, 2022

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