A hot-air balloon is 140 ft140 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi divided by hr60 mi/hr (88 ft divided by s88 ft/s). if the balloon rises vertically at a rate of 14 ft divided by s14 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 10 seconds10 seconds later?

Step-by-step explanation:

Given

Balloon velocity is 14 ft/s upwards  

Distance between balloon and cyclist is 140 ft

Velocity of motor cycle is 88 ft/s

After 10 sec  

motorcyclist traveled a distance of

Distance traveled by balloon in 10 s

net height of balloon from ground =140+140=280 ft[/tex]

at

distance between cyclist and balloon is

now suppose at any time t motorcyclist cover a distance of x m and balloon is at a height of h m

thus

differentiating w.r.t time

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.