- #1
mmiller39
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This is a problem from Cutnell and Johnson Physics
I have set up my formula so that eventually I am solving a quadtratic equation, I am unsure if my calculations are correct, any input would be appreciated.
THE QUESTION:
An airplane is flying with a velocity of 240 m/s at an angle of 30.0° with the horizontal. When the altitude of the plane is 2.4 km, a flare is released from the plane. The flare hits the target on the ground. What is the angle ?
WHAT WE KNOW:
Vo: 240 m/s
y = 2.4 km
Theta: 30 degrees
Beta : The unknown angle
MY CALCULATIONS:
Vo Sin 30 = Voy = -120 m/s (because it is in a downward direction, I think)
y = Voy(t) + 1/2ay(t^2)
-2,400 = -120(t) + 1/2(-9.80)(t^2)
In quadratic Form:
-4.9t^2 - 120(t) + 2,400 = 0
t = -120 +/- Sqrt (120^2 - 4(-4.9 x 2400))/2 x -4.9
THIS IS WHERE I GET CONFUSED
I am unsure if my signs are correct or if I am solving the formula correctly. I will go ahead and show the rest of my calculations but they are incorrect. (or could have been from the beginning)
t = 13.04 s
Vo cos 30 = Vox = 207 m/s
x = Vox(t) = 2699 m
Beta = tan^-1 y/x = tan^-1 2,400/2,699 = 41.64 degrees. <-----
*this answer is wrong, I am unsure where I made my error(s). Any help is greatly appreciated.
I have set up my formula so that eventually I am solving a quadtratic equation, I am unsure if my calculations are correct, any input would be appreciated.
THE QUESTION:
An airplane is flying with a velocity of 240 m/s at an angle of 30.0° with the horizontal. When the altitude of the plane is 2.4 km, a flare is released from the plane. The flare hits the target on the ground. What is the angle ?
WHAT WE KNOW:
Vo: 240 m/s
y = 2.4 km
Theta: 30 degrees
Beta : The unknown angle
MY CALCULATIONS:
Vo Sin 30 = Voy = -120 m/s (because it is in a downward direction, I think)
y = Voy(t) + 1/2ay(t^2)
-2,400 = -120(t) + 1/2(-9.80)(t^2)
In quadratic Form:
-4.9t^2 - 120(t) + 2,400 = 0
t = -120 +/- Sqrt (120^2 - 4(-4.9 x 2400))/2 x -4.9
THIS IS WHERE I GET CONFUSED
I am unsure if my signs are correct or if I am solving the formula correctly. I will go ahead and show the rest of my calculations but they are incorrect. (or could have been from the beginning)
t = 13.04 s
Vo cos 30 = Vox = 207 m/s
x = Vox(t) = 2699 m
Beta = tan^-1 y/x = tan^-1 2,400/2,699 = 41.64 degrees. <-----
*this answer is wrong, I am unsure where I made my error(s). Any help is greatly appreciated.