Question

MEDAL!!!



A ball is thrown straight up. What will be the instantaneous velocity at the top of its path? What will be its acceleration at the top? Why are your answers different?

Answer 1

@jim_thompson5910

Answer 2

Is it not that when it goes upward, at the top of its path, velocity =0?

Answer 3

OOOPS is correct

Gravity is pulling the ball down. The initial throw pushes the ball up and the velocity decreases as the ball climbs higher because it's fighting gravity. Once the ball gets to the peak, the velocity hits 0. The acceleration due to gravity is always the same no matter how fast the ball is moving.

Answer 4

What would be its acceleration?

Answer 5

The acceleration due to gravity is always the same no matter how fast the ball is moving.

acceleration of gravity = 9.8 m/s^2 = 32 ft/s^2 (both are approximate)

Answer 6

How did you calculate that 9.8m/s^2 = 38ft?s^2 ?

Answer 7

the acceleration of gravity only changes when the height is drastically different

technically there is change, but it's so small that it's hard to notice

Answer 8

it's just something you look up in a table, book, or something.

or you memorize it

Answer 9

I mean i know that 9.8m/s^2 is the instantaneous speed of a free-falling object. but how did you just calculate the acceleration at the top?
acceleration = gravity x time ?

Answer 10

the acceleration is equal to the acceleration of gravity

Answer 11

Honestly, i have no idea to what you just said.

Answer 12

imagine the object in free fall

every second, the speed increases by 9.8 m/s

Answer 13

okay

Answer 14

let t be the time elapsed since dropping the object and letting it free fall (ignore air resistance)

t = 0
speed = 0 m/s

t = 1
speed = 9.8 m/s

t = 2
speed = 19.6 m/s (9.8 times 2 = 19.6)

t = 3
speed = 29.4 m/s (9.8 times 3 = 29.4)

etc etc

Answer 15

yeah...

Answer 16

so what's going to happen next?

Answer 17

No matter where the object is, it's feeling the same force on it. So it undergoes the same acceleration throughout its journey going up and then coming back down

Answer 18

acceleration is a vector. i.e. it has direction.

Answer 19

but my question was how did you get this:
"acceleration of gravity = 9.8 m/s^2 = 32 ft/s^2 (both are approximate)"

Answer 20

Isac Newton

Answer 21

I think...

Answer 22

Galileo discovered it long before Newton, but yeah pretty much

Answer 23

did he discover the speed or just the thing?

Answer 24

those two numbers are constants that you memorize or look up

Answer 25

so the acceleration is 32?

Answer 26

32 ft per s^2, yes

Answer 27

just the speed/acceleration I think @zzr0ck3r

I don't think he actually came up with unifying theories like Newton did

Answer 28

And almost got killed as a result. Ahh humans...

Answer 29

so i found this website where it said that the acceleration can just be defined as "g", i believe:

Answer 30

yes. gravity is constant and we normally just say g because we are estimating it when we give an actually number.

Answer 31

like \(\pi\) and 3.14. They are not the same but we use 3.14 when we need a close number.

Answer 32

g = 9.8 m/s^2

or

g = 32 ft/s^2

both are the same. Saying 'g' is a shorthand way to say "acceleration of gravity on earth at sea level"

Answer 33

When you hear things like "the rocket is going 3 g's (idk I made up the number)" it means "the rocket is accelerating 3 times the acceleration of gravity"

so the rocket's acceleration would be 29 m/s^2

Answer 34

Thank you. I have another question.

Answer 35

If you have time and are interested, see
https://www.khanacademy.org/science/physics/newton-gravitation/gravity-newtonian/v/introduction-to-gravity

Answer 36

If a salmon swims straight upward in the water fast enough to break through the surface at a speed of 5m/s, how high can it jump above the water?

Answer 37

Acceleration of gravity:
g = 9.8 m/s^2

Initial Velocity
Vo = 5 m/s

Plug those values into

h = -(g/2)t^2 + Vo*t

We don't know anything about the angle in which it jumps, so ignore that. Assume it jumps straight up. Find the vertex to get the answer.

Answer 38

h = (-9.8/2)5^2 + 5*2

Answer 39

t is unknown for now

Answer 40

Yeah that's what I was guessing

Answer 41

you should get

h = -4.9t^2 + 5t

find the vertex of this to figure out the highest point

Answer 42

How would I figured out the vertex?

Answer 43

*figure

Answer 44

h = -4.9t^2 + 5t is in the form h = at^2 + bt + c

a = -4.9
b = 5
c = 0

plug the values of 'a' and 'b' into -b/(2a) to figure out the time value at the peak

once you get this value, plug it into h = -4.9t^2 + 5t to find h

Answer 45

so t would be -b/(2a) ?

Answer 46

the t value at the peak, yes