Modeling Projection Motion Problem - Calc 3

[Will15]

Homework Statement

A person is standing 80 ft from a tall cliff. She throws a rock at 80 ft/sec at an angle of 45 degrees from the horizontal. Neglecting air resistance and discounting the height of the person, how far up the cliff does it hit?

Homework Equations

r = ((xo + vo*cos(~))t) i + (yo + (vo*sin(~)t - ((1/2)gt^2))j
r = the distance ; xo = initial distance from horizontal direction ; yo = initial distance from vertical direction ; vo = initial velocity; t = time; g = gravity (9.8m/s); ~ = degrees

The Attempt at a Solution

The correct answer is 48 feet. I did not get that answer from plugging in all the values in the equation.

 

[Villyer]

What exactly did you plug in?

Your listed gravity was in m/s, although all given measurments were in feet. Is it possible that the numbers weren't converted?
Also, your equations have time in them, and you never mentioned how you solved for time.

 

[Will15]

What exactly did you plug in?

Your listed gravity was in m/s, although all given measurments were in feet. Is it possible that the numbers weren't converted?
Also, your equations have time in them, and you never mentioned how you solved for time.

Man that was it! I didn't convert the m/s into ft/s!

For time, I used the first part of the equation r = xo + (vo*cos~)t => 80/(80*cos45) = t = 1.414
Then I just plugged this into the second equation r = yo + (vo*sin~)t-(.5)(g)(t^2) => r = (80*sin45)(1.414)-(4.9)(1.414)^2) = 70.2ft is the answer i gotten.

If I replace 4.9 with the converted ft (32.1522) I would get ~48ft!

Thanks bud!

 

[klondike]

The problem can be solved algebraically. Just get rid of t, express vertical displacement in terms of v,g, vertical distance, and angle. A little extra pain is converting dead King's finger unit to SI back and forth. And if you are using calculator to find sin(), cos(), and you were entering 45, make sure it's in degree mode.