# Projectile motion and angle

terryaki
I need help putting this problem into a workable equation:

A projectile is launched from ground level at an angle of 12 degrees above the horizontal. It returns to ground level. To what value should the launch angle be adjusted, w/o changing the launch speed, so that the range doubles?

So far I tried this:

I broke the problem into its components: x & y.
FOR X: {x=Vo*COS(12)t Vox=Vo*Cos(12) a=0 t=t}
FOR Y: {y=? Voy=Vo*SIN(12) a=-9.8 m/s^2 t=t}

Then I used t=x/Vo*COS(12), then substituted that for T in the Y parts, so that:

y= tan(12)x - [(4.9 x^2)/(Vo^2*cos(12)^2)]

but then I got: x=tan(12)y, which doesn't help me at all.

I'm guessing I'm approaching this problem in a totally WRONG way!

dduardo
Staff Emeritus
so you start out with a vector v-> and an angle theta1.

x = |v->| * cos(theta1) * t
y = |v->| * sin(theta1) * t - (1/2) * g * t^2

when y = 0, the projectile will be on the ground

0 = |v->| * sine(theta1) * t - (1/2) * g * t^2

t = 0 , 2 *|v->| * sin(theta1) / g

when t = 0 is at the start, so the other solution is the time it hits the ground

x = |v->| * cos(theta1) * 2 *|v->| * sin(theta1) / g

pluging in t into the x equation and doing some math you get:

x = |v->|^2 * sin( 2 * theta1) / g

If you want the range to be double then it is 2 times the x equation with the new angle.

x2 = 2 * |v->|^2 * sin( 2 * theta2) / g

equate x and x2 to find theta2. You know theta1 = 12 degrees

x = x2 , then theta2 = 5.87 degrees