A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235m below. If the plane is traveling horizontally with a speed of 250 km/h (69.4m/s), (a) how far in advance of the recipients ( horizontal distance) must the goods be dropped. (b) Suppose, instead that the plane release the supplies a horizontal distance of 425m in advance of the mountain climbers. What vertical velocity (up or down) should the supplies be given so that they arrive precisely at the climber's position? (c) with what speed do the supplies land in the latter case

Explanation:

For vertical displacement of food-supply

if time taken to reach the ground be t

235 = 1/2 g t²  , initial velocity downwards is zero.

t = 6.92 s

Horizontal displacement of food during this period

= 6.92 x 69.4 m

= 480.25 m .

b )

time required to cover horizontal distance of 425 m

= 425 / 69.4 = 6.124 s  

This time period will be the time of vertical fall of 235 m . Let initial vertical velocity required be u

h = ut + 1/2 gt²

235 = u x 6.124 + .5 x 9.8 x 6.124²

235 = u x 6.124 + 183.76

u = 8.36 m /s

c )

v = u + gt

= 8.36 + 9.8 x 6.124

= 68.37 m /s

This will be vertical component of velocity .

horizontal velocity = 69.4 m /s

resultant velocity = √ ( 68.37² + 69.4²)

= √(4674.45 +4816.36)

= 97.42 m /s

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.