A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 45 degrees. At what rate, in km/min, is the distance from the plane to the radar station increasing 2 minutes later?
Rate = km/min
The vertical coordinate (in km) from the radar station is
Y = 4 + 0.707*24 t
and the horizonal coordinate is
X = 0.707*24 t
where t is in minutes.
The distance between radar station and plane is
R = sqrt (X^2 + Y^2)
take the time derivative to get dR/dt and then plug in t = 2 for the answer.
can you give me some homework about that
Sure! Here's a homework problem related to the scenario you described:
A car is driving on a straight road at a constant speed of 60 km/h. There is a point P on the side of the road, and the angle between the car's path and the line connecting the car to point P is 30 degrees. At time t = 0, the car is 200 meters away from point P.
1. Determine the horizontal coordinate X(t) and vertical coordinate Y(t) of the car as functions of time, t, in minutes.
2. Write an equation for the distance, R(t), between the car and point P as a function of time.
3. Find the rate at which the distance between the car and point P is decreasing 5 minutes later. (In other words, find dR/dt at t = 5 minutes).
To solve this problem, you can use the given information to set up equations similar to the ones we used in the previous question. Remember to convert the car's speed from km/h to km/min.