PROJECTILE TIME FORMULA

Requires: Final velocity, acceleration, angle, and height. Gives: Time

Variable info

♦ INITIAL VELOCITY (V_o)
♦ ANGLE (A°)

♦ GRAVITY (earth is 9.8 _m/s) (g)
♦ HEIGHT (h)

Welcome, today we will learn how to figure out the time variable after a projectile is launched. Lets say if for example

you threw a ball. We can calculate the exact amount of time with velocity, gravity, height, and angle.

Lets start with a formula...

-V_osin(A°) ± √(V_o-sin(A°))² + 2gh)

Now lets make up some numbers, this will be diffrent from the illustration to the left.

♦ V_o = 30_m/s
♦ Angle = 90°

♦ Gravity = 9.8_m/s
♦ Height = 10 _meters

Great, now that we have all of our variables, lets plug them in.

-30(1) ± √((30-1)² + 2(9.8_m/s)(10_m))

9.8_m/s

♦We'll be doing parenthesis first, due to PEMDAS.

-30(1)±√((29)²+2(9.8)(10)

9.8

♦Now that we've done that, we'll go onto exponets.

-30(1)±√(841+2(9.8)(10)

9.8

♦Easy right? Next, lets do the multiplication now.

-30±√841+196

9.8

♦ We're almost done, lets add 841 and 196.

-30±√1,037

9.8

♦Next, we'll find the square root of 1,037. Which is

32.2~

Current result:

-30±1,037

9.8

Great! We got it down to the last few steps. Heres what we're gonna do

♦We will split into two, the first equation will replace the plus-minus sign with a plus, and vice versa.

♦We'll add/subtract the first two top numbers

♦Divide

Now we should be left with two numbers from both equations.

♦You should have a negative and a positive number. Logic states we cant have objects falling with negative time. So the positive answer is correct

Now lets get down to business now that we have our steps.

♦ First split into two...

-30+1,037

9.8

AND

-30-1,037

9.8

♦ Then add/subtract the top two numbers.

1,007

9.8

AND

-1,069

9.8

♦ Finally, we divide.

102.75~

AND

-109.08~

♦ Logically, we cant have time being negative, we've resulted with a negative and a positive. That means the answer is

102.75~

Now that we have the answer, we can optionally check our work, this is the roadmap we will follow in order to check our work.

♦Find V_f _{(Final Velocity) with the formula:}

V_f=V_o+a*t

♦ Then we will find acceleration with the following formula:

V_f-V_o

♦Why are we finding aceleration again you may ask? Well if its equal to 9.8_m/s then we just went into a loop, meaning we're correct about time.

Lets begin plugging in the numbers and trying to find V_f

V_f=30+9.8_m/s*102.75~

We shouldn't need any major steps or instruction for a formula such as this, the answer is

1036.95~

Now that we have our answer, we can calculate acceleration since it requires V_f

1036.95-30 102.75

Once again, if you can handle a monster equation such as time, you should be able to handle this one. The answer is

9.8

Hope this helped _{(it didn't)}

ok im going to sleep now.