Ashell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff. the shell strikes the ground 1330 m from the base of the cliff. the drawing is not to scale.

Missing question:

What is the initial speed of the shell?

329.2 m/s

Explanation:

The motion of the shell is a projectile motion, consisting of:

- A uniform motion along the horizontal direction, with constant velocity

- A uniformly accelerated motion along the vertical direction, due to the force of graviity

We start by analyzing the vertical motion first. The shell falls down due to the effect of gravity, so we can use the following equation:

where, taking downward as positive direction:

s = 80 m is the vertical displacement of the shell (= the height of the cliff)

u = 0 is the initial vertical velocity

t is the time of flight

is the acceleration of gravity

Solving for t, we find the time of flight:

Now we know that along the horizontal direction, the shell travels a distance of

d = 1330 m

And it takes a time of

t = 4.04 s

We know that the horizontal velocity is constant, so we can find it as:

And since it is constant during the entire motion, this was also the initial horizontal velocity of the bullet.

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.  

asthenosphere and convection