"A weather balloon that is dropping vertically is being observed..."

[clayc213]

1.A weather balloon that is dropping vertically is being observed from a point on the ground 2 miles from the spot directly beneath the balloon. At what rate is the balloon descending when the angle between the ground and the observers line of sight is pi/5 and decreasing at 0.2 radians per minute?

2. Two straight roads intersect at right angles. at 10 AM a car passes through the intersection headed due east at 30mph. at 11 AM a truck heading due north at 40mph passes through the intersection. At what rate are they separating at 1 PM.


I always have trouble with word problems like this. Any help is appreciated!!

 

[stapel]

Use what you learned back in algebra:

1.A weather balloon that is dropping vertically is being observed from a point on the ground 2 miles from the spot directly beneath the balloon. At what rate is the balloon descending when the angle between the ground and the observers line of sight is pi/5 and decreasing at 0.2 radians per minute?

You drew the horizontal line for the ground, the vertical line for the balloon's path, and the slanty line between the balloon and the ground observer. You labelled the ground distance as 2 and the height as "h". You noted the right triangle, and labelled the base angle A, noting that dA/dt = -0.2 radians/min. You noted the trig ration which allows for an equation, and... then what?

2. Two straight roads intersect at right angles. at 10 AM a car passes through the intersection headed due east at 30mph. at 11 AM a truck heading due north at 40mph passes through the intersection. At what rate are they separating at 1 PM.

You drew a vertical and an horizontal line, crossing in the middle. You drew a dot on the positive x-axis for the car, and labelled the distance with the fixed one-hour distance, plus the per-hour rate. You drew a dot on the positive y-axis for the truck, and labelled the distance with the per-hour rate. You drew the line for the distance between the two vehicles. You noted the right triangle, and... then what?