Solve Algebra Question: Projectile Fired at 30m/s, Angle 60°, 7.5s Later

[doucette1717]

Homework Statement

A projectile is fired with an initial speed of 30 m/s at an angle of 60 degrees above the horizontal. The object hits the ground 7.5 s later.
knowns: x0=y0=t0= 0, v0=30 m/s, t2= 7.5 s, angle= 60 degree, ay= -9.8 m/s, v1y=0, and v1x=v0x=v2x...find: y2-y0 y1-y0 and v2 angle

Homework Equations

1# vy2= y0 + v0y(t2-t0)+ 1/2ay(t2-t0)^2
2# v1y^2=v0y^2 + 2ay(y1-y0)

The Attempt at a Solution

I've found y2=-80.8 meters and am currently trying to figure out y1. I am using equation #2 and have this 0m/s^2= (30sin60m/s)^2 +2(-9.8m/s^2)(y1-0m) = y1= 34.4 m. I know the answer, but am having trouble isolating y1, i.e. not sure how to do the algebra. Everytime i attempt it, i get the wrong answer. any help will be appreciated, thanks.

 

[tiny-tim]

Welcome to PF!

1# vy2= y0 + v0y(t2-t0)+ 1/2ay(t2-t0)^2
2# v1y^2=v0y^2 + 2ay(y1-y0)

3. The Attempt at a Solution
I've found y2=-80.8 meters and am currently trying to figure out y1. I am using equation #2 and have this 0m/s^2= (30sin60m/s)^2 +2(-9.8m/s^2)(y1-0m) = y1= 34.4 m. I know the answer, but am having trouble isolating y1, i.e. not sure how to do the algebra. Everytime i attempt it, i get the wrong answer. any help will be appreciated, thanks.

Hi doucette1717! Welcome to PF!

(I assume y1 is the maximum height.)

Your y2 = -80.8 and y1 = 34.4 seem to be correct.

So I don't understand what answer you're not getting.

Show us the algebra you're having trouble with.

 

[doucette1717]

Hi doucette1717! Welcome to PF!

(I assume y1 is the maximum height.)

Your y2 = -80.8 and y1 = 34.4 seem to be correct.

So I don't understand what answer you're not getting.

Show us the algebra you're having trouble with.

Well the problem is with this 0m/s^2= (30sin60m/s)^2 +2(-9.8m/s^2)(y1-0m) = y1= 34.4 m.
i was given the answer, i myself don't understand how to isolate y1 and do the math to get 34.4 m.

 

[tiny-tim]

Well the problem is with this 0m/s^2= (30sin60m/s)^2 +2(-9.8m/s^2)(y1-0m) = y1= 34.4 m.
i was given the answer, i myself don't understand how to isolate y1 and do the math to get 34.4 m.

oh I see …

well, you have 0 = (30sin60m/s)^2 +2(-9.8m/s^2)(y1-0m)

ie 0 = (30*0.866)² + 2*-9.8*y1,

so y1 = (30*0.866)²/2*9.8 = 34.4.

what was worrying you?

 

[doucette1717]

i have a test coming up soon. My math skills aren't the greatest. Just trying to improve them so i can do better on my test. Thanks.

update:
so i tried the calculation you gave me and i got 3307. m. I'm not sure what I am doing wrong either, i plugged those exact values right into my calculator.

 

[tiny-tim]

i have a test coming up soon. My math skills aren't the greatest. Just trying to improve them so i can do better on my test. Thanks.

update:
so i tried the calculation you gave me and i got 3307. m. I'm not sure what I am doing wrong either, i plugged those exact values right into my calculator.

Hi doucette!

That's because you plugged in ((30*0.866)²/2)*9.8 instead of (30*0.866)²/2*9.8.

Tip: If you're using a cacluator, it's easy to go wrong, so always check that the result is roughly correct …

in this case, you know it's roughly 30*30/2*10 = 45 … so 3307 is obviously about 100 time too much!

Another tip: if I'm using a calculator, I do the bottom line first, then I press "1/x", then I do the top line!