Question

@hartnn
a ball is thrown at a speed of 10m/s. Mass of ball = 3 kg
It is aimed towards a fan with 3 blades. Fan is moving at an angular velocity of 5 rad/sec . 1 blade of fan = 1 m .
It is aimed towards the center of fan at a distance of 5 m. What is the probability that ball with cross the fan ?
Its related to parabolic motion

Answer 1

this problem is a lot easier than it sounds

Answer 2

first you need to realize that the mass of the ball is irrelevant so you can forget about that

Answer 3

@hartnn see, @ekmath is going to solve it. learn

Answer 4

you also need to remember that when we are dealing with projectiles, they always have parabolic motion.

Answer 5

have you learned about vectors?

Answer 6

yes, bit..few years ago.

Answer 7

a few years ago? how old are you? (not trying to be creeping at all just want to know what course you saw this question in)

Answer 8

I am 22 years old and I am teaching in a primary school. revising all this.

Answer 9

@ekmath ??
we are teaching @hartnn here..
don;t embarras me :|

Answer 10

should i click on that?

Answer 11

i never said i wanted to learn that.

Answer 12

click on that?

Answer 13

ok so when something is in projectile motion it has an x vector (left-right) and a y vector(up and down) vector means the direction that it is traveling in. both of these combined give it parabolic motion

Answer 14

yes.

Answer 15

you with me? so the x velocity(speed) is a constant because there is nothing acting against it. the ball is moving towards the fan in a left-right sense at 5 m/s the whole time

Answer 16

but it'll come down also

Answer 17

the y velocity is not a constant because there is gravity that is bringing it down

Answer 18

yes.I follow what you say

Answer 19

great, so we need to see if, in the time it takes for ball to travel the distance towards the fan (in the x sense, which is 5 meters) , if the ball drops below the fan blade

Answer 20

yes

Answer 21

so when looking at the x vector we will use the distance formula.
d = rt
distance = rate x time
5m = 5(m/s) x t
divide out 5 to get that t = 1 second

Answer 22

yes. right
so ball reaches the fan in 1 second
but we do not know the height yet
certainly iy'll be down a bit

Answer 23

so now we need to see how far the ball drop (talking about the y now) in 1 second

Answer 24

the standard equation is s=(v0)t + .5(a)(t^2)

Answer 25

newtons equation of motion

Answer 26

a=10 or -10 ?

Answer 27

v0 is the initial velocity in the y (down) direction. because you are throwing it straight across v0 is 0

Answer 28

well its 9.8 but 10 is a whole lot easier.

Answer 29

its hinted here to use 10

Answer 30

the minus or plus all depends on if you consider something going down to be a negative velocity

Answer 31

taking negative would be more convenient right? since its going down

Answer 32

so if we plug that in... ("s" is a term for distance btw)

we get
s = 0 + .5(10)(1^2)
so s=5
the fan blade is 1 meter so it misses the fan by about 4 meters

Answer 33

all good?

Answer 34

ohh

:O

so answer = 0?

Answer 35

yup

Answer 36

omg! great!
so we never had to check for the motion of the fan!

Answer 37

also, the problem never gave you the blade length or the ball size so even it did hit the fan it would be imposible to figure out.

Answer 38

oh okay

Answer 39

thank you

Answer 40

no prob

Answer 41

what?