Question

A cannonball is shot at an angle of 45 degrees to the horizon with a velocity of 100m/s.
a. how high above the ground will it get?
b. how far away from the cannon will it hit the ground?
c. at what velocity will it hit the ground?

Answer 1

First step is to use vectors to determine the vertical (y) component of the cannon balls acceleration

I can draw a diagram if you want

Answer 2

yes please

Answer 3

sweet gimme a second

Answer 4

How do you think you would find Y?

Answer 5

you take the sin of 45 degrees and multiply by 100 right?

Answer 6

Yup! now we have the vertical component of velocity, we can find how high it will get using kinematic equations

Are you familiar with kinematic equations?

Answer 7

not really haha

Answer 8

Sweet as, we know the initial velocity, the acceleration of the cannonball (which is the acceleration of gravity 10 ms^-2), the final velocity ( which is zero at its highest point) and want to find the distance traveled.

we can look at some kinematic equations, and find one that has those terms, then use it to find distance.

http://www.physicsclassroom.com/class/vectors/u3l2e3.gif

look at these and find one that has, initial velocity, final velocity, acceleration and displacement

Answer 9

the 3rd equattion

Answer 10

Nice! so first off lets just get rid of Vf^2, as we know its zero haha

this give us a nice equation 0 = Vi^2 + 2ad

rearranging for d ( which is the distance we want) we get -Vi^2 / 2a = d

Answer 11

now just plug in Vi and a, and you will get d, which is the vertical distance the cannonball will travel

Answer 12

vi is 100 and acceleration is -9.81 right?

Answer 13

sure is

Answer 14

so its 509.68 ?

Answer 15

yup well done

Answer 16

For the second question we need the time that that ball will be in the air, so find an equation from that page i linked you that gives us the time, relative to acceleration and velocity.

Answer 17

wait so which part did we just answer?

Answer 18

Part a! we found the vertical distance that the cannonball with travel

Answer 19

oh ok gotcha haha!

Answer 20

and the second equation right?

Answer 21

So now we want to find the distance traveled in the x direction

Answer 22

yup the second equation is correct

Answer 23

so vf=vi+a*t?
vf is 100
a is -9.81
and we have to solve for t still?

Answer 24

we sure do. that gives us half the time that the ball spends in the air, so the time the ball takes to get to its maximum height

Answer 25

we double time

Answer 26

yup, if we double time, it gives the the entire time that the ball is in the air, which means we can calculate the distance traveled in the x direction during that time using the first equation

Answer 27

i got t=-10.19

Answer 28

yup, except time is positive in this case, so we can drop the negative sign to get 10.19 seconds

Answer 29

so thats the time for the ball to get to its highest point, and it will take the same amount of time to get back down again, so double that time for the total flight time!

Answer 30

20.38?

Answer 31

yup, so what else do we need for the first equation that we dont already have? (its only one more thing)

Answer 32

vi and thats 0 right?

Answer 33

we do need Vi, but Vi is not zero

Answer 34

Think of how we found Vi for the first question

Answer 35

ooooooh so its cos(45)x100

Answer 36

and thats 85.09

Answer 37

yup! well done!

Answer 38

thank you!

Answer 39

no problem, now plug all your values into the first equation to find the distance traveled

Answer 40

do i still square the time like how it says in the last part or do i multiply time by 2

Answer 41

always just do what the equation tells you, so in this case square time. We have already doubled time to get 20.38 seconds remember.


What value are you using for a? ( acceleration)

Answer 42

-9.81?

Answer 43

What direction does gravity work?

Answer 44

x or y?

Answer 45

y...

Answer 46

i got d=357.75m

Answer 47

So if gravity works in the y direction, do you think that it would have any effect on the distance traveled in the x direction?

Answer 48

remember we are trying to find the distance traveled in the x direction

Answer 49

well yes because if it wasnt it would just keep going? a force has to bring it down right?

Answer 50

Gravity determines the time the ball is in the air, but has no effect on the horizontal velocity

Answer 51

As there are no forces acting on the ball in the x direction, there is no acceleration of the ball in the x direction. For the second question acceleration is therefore zero.

Answer 52

its asking how far from the cannon will it hit the ground, so gravity doesnt matter here?

Answer 53

we are working in the x direction, gravity only effects y direction

Answer 54

so its just d= (85.09)(10.19)+1/2(0)(10.19)^2?

Answer 55

yup sure is

Answer 56

except time is double remember

Answer 57

so t = 20.38

Answer 58

d=1734.1342?

Answer 59

Nicely done

Answer 60

seems like its too big of a number though..

Answer 61

is the unit meters?

Answer 62

Yup

Answer 63

remember that the ball is traveling at 360km/h or 223mph

Answer 64

wait where did that number come form

Answer 65

from

Answer 66

I just converted from 100m/s to km/h

Answer 67

dont worry about it if its confusing, just trust me that it's the right answer haha

Answer 68

oh ok

Answer 69

lol okay ill trust you

Answer 70

ok, final question! no calculations needed for this one, how fast do you think it will be traveling when it hits the ground?

Answer 71

i have no idea

Answer 72

well we know the horizontal velocity stays the same, because no forces act on the ball in the horizontal direction.

for the vertical we know the ball only every experiences one force, gravity, which is the same for when the ball is going up, and coming back down.

so the ball will slow down, stop at the top, then start accelerating back to earth and be at tis initial velocity again once it reaches the ground!

Answer 73

soo we factor in -9.81 to vy?

Answer 74

yeah, but its the same going up and down, so the final velociy is the same as the initial velocity, 100 m/s

Answer 75

ok so how would the equation look

Answer 76

complicated.

Answer 77

so what do i do

Answer 78

your answer for c is 100m/s

Answer 79

ok haha

Answer 80

if asked to explain it by your teacher, just say you thought about conservation of energy

Answer 81

ek = 1/2mv^2

Answer 82

alright haah i have 2 more questions could you help ?

Answer 83

how old are you?

Answer 84

if you dont mind me asking

Answer 85

17

Answer 86

why. how about you

Answer 87

21