Question

A person is standing 75 meters away from a kite and has a spool of string attached to the kite. The kite starts to rise straight up in the air at a rate of 2 m/sec and at the same time the person starts to move towards the kites launch point at a rate of 0.75 m/sec. Is the length string increasing or decreasing after (a) 4 seconds and (b) 20 seconds.

Answer 1

After 4 seconds, the length of the string attached to the kite is decreasing by 5 meters. After 20 seconds, the length of the string is increasing by 55 meters.

Step-by-step explanation:

To determine whether the length of string attached to the kite is increasing or decreasing, we need to consider the vertical and horizontal movements.

(a) After 4 seconds, the person has moved a distance of (0.75 m/sec) * (4 sec) = 3 meters towards the kite's launch point. At the same time, the kite has risen vertically at a rate of 2 m/sec for 4 seconds, reaching a height of (2 m/sec) * (4 sec) = 8 meters. Therefore, the length of the string is decreasing by (8 meters - 3 meters) = 5 meters.

(b) After 20 seconds, the person has moved a distance of (0.75 m/sec) * (20 sec) = 15 meters towards the kite's launch point. The kite has risen vertically at a rate of 2 m/sec for 20 seconds, reaching a height of (2 m/sec) * (20 sec) = 40 meters. Therefore, the length of the string is increasing by (40 meters + 15 meters) = 55 meters.