Question

Projectile fired...again

Answer 1

Projectile is fired at intial speed of v0 ft/s at an angle alpha above the horizontal, then its position after t seconds is given by the following parametric equations where x and y are measured in feet. By eliminating the parameter t, it can be shown that the path is a parabola.
x= (vocos(alpha)t, y=(vosin(alpha))t-16t^2

Answer 2

Suppose a gun fires a bullet into the air with an initial speed of 2048 ft./s at angle 30 degrees to the horizontals.

Answer 3

a)after how many seconds will the bullet hit the ground?
b) how far from the gun will the bullet hit the ground?
c) what is the maximum height atttained by the bullet?

Answer 4

@rational :)

Answer 5

Hint : y is 0 when the bullet hits the ground

Answer 6

so i use the second equation and set y to 0?

Answer 7

but first I have to find t. but doing question a

Answer 8

yes set y equal to 0 and find t

Answer 9

y=(vosin(alpha))t-16t^2

0=(vosin(alpha))t-16t^2

plugin the given values and solve t

Answer 10

what does it mean when it says algebraically?

Answer 11

ah, so I do b first? okies.

Answer 12

we're doing a first

Answer 13

a)after how many seconds will the bullet hit the ground?


this is about finding time only right

Answer 14

b is about finding the x value

Answer 15

x : horizontal distance
y : time

Answer 16

oh oh gotcha.

Answer 17

err so
0=t(2048sin30 - 16t)

Answer 18

divide both sides by t
0=2048sin30-16t

Answer 19

t=2048sin30/16 ?

Answer 20

=64

Answer 21

yes!

Answer 22

bullet hits the ground after 64 seconds

Answer 23

okies
and then the answer to b is 21.498 miles?

Answer 24

Yep!

Answer 25

andd c= 10.749 miles?

Answer 26

oh wait, I don't think that's correct. I just divided x by 2 but didn't replug it into the equation

Answer 27

10.749 is the x axis at maximum height but idk the y

Answer 28

forget about x

Answer 29

it took 64 seconds for the entire journey, right ?

Answer 30

yeah. so 32 until max height

Answer 31

yes simply plugin t=32 into the equation for y

Answer 32

the equation where y = 0?
or just the right side of the y one

Answer 33

y=0 corresponds to the height when the bullet hits ground

Answer 34

so how is that related to the maximum height ?

Answer 35

ok, so the answer i'm getting is 16384
divided by 5280 to get miles = 3.103

Answer 36

yeah, sorry, that was an uneducated comment :P

Answer 37

looks good!

Answer 38

Fantastic:) thank you so much!

Answer 39

yw