# Projectile Motion - Is my work correct?

## Homework Statement

You drop a ball (0.5kg( from a height of 4m. How long did the ball take to hit the ground?

## Homework Equations

Assume that initially the velocity is 0 for the following equations below.
$$\Delta$$Position = $$\Delta$$ Velocity * $$\Delta$$ Time
Acceleration = $$\Delta$$ Velocity / $$\Delta$$ Time

## The Attempt at a Solution

Acceleration is -10m/s due to gravity.
$$\Delta$$X = $$\Delta$$ V * $$\Delta$$ T
4 = $$\Delta$$ V * $$\Delta$$ T
4 = V * (V/10)
4 = V2/10
40 = V2
Root(40) = V

Then just plug in and solve for time.

Root(40)/(10m/s) = $$\Delta$$T
$$\Delta$$T is approximately .63 seconds.

I don't know if this is right.. seems like a short amount of time to be honest.

Delphi51
Homework Helper
I don't follow your calc. Looks like you tried to use the TEX code and it messed up. I can't seem to do TEX, either. I'm a retired high school teacher so I do really basic solutions. We know d and want t, the motion is accelerated at g. So we need an accelerated motion formula with d and t in it, but not Vf because we don't know the final velocity and don't need to find it. We do know that the initial velocity is zero. That leaves good old d = Vi*t + ½a*t². Cross out the Vi*t term because Vi is zero. Solve the equation for t. I get slightly less than 1 second.

Using that I got .89 seconds..
I wonder why my solution is incorrect though.
And sorry about the messed up formatting, I didn't realize it was like that..
After all that effort i put in to use the TEX code.. oh well.

Why would this not work? All I'm doing is substituting variables.

A = 10m/s due to grav
D = 4

4 = Velocity * Time
Velocity/ Acceleration = Time
Velocity / 10 = Time

4 = Velocity * Velocity/10
40 = Velocity^2

Then plug that value into V/A = T
T = approximately .63

Delphi51
Homework Helper
It isn't correct to use "4 = Velocity * Time". The formula d = vt does not apply to accelerated motion. You should have a formula sheet like this:

Motion at constant speed: d = vt
Accelerated motion: d = Vi*t + ½a*t², a = ΔV/Δt, V = Vi + a*t

In any problem, the first thing you figure out is what kind of motion is involved so you know which formula(s) apply.

I got 0.903 s but I used g = 9.81 instead of your g = 10.

That makes sense.
Silly me, I forgot about that..
Thank you! I'll be sure to use that list of formulas.

Delphi51
Homework Helper
Most welcome.
Add to your list of formulas as you go. When you get more exotic formulas, be sure to write the explanation right beside the formula so you remember them together:
F = ma, a = F/m A force causes a mass to accelerate.
Ek = ½mv² Velocity gives a mass kinetic energy

Hi
I am doing my engineering degree and i am stuck on a question i came to the conclusion that the text book must be wrong . lectures are over and test is soon . can you please help?

A projectile is thrown upwards and passes a certain height after 2 seconds.3seconds later it passes the same pont again.calculate the height of the point above the ground