Missile Launch

Formulas and examples

Velocity in x and y direction

• General:• X component of original velocity: vox =

vocos(theta)

• Y component of original velocity: voy = vosin(theta)

θ

Example 1

• In the x direction:• vox = vocos(theta)

• vox = (40.0 m/s)(cos(35 degrees))

• vox = (40.0)(0.8191)

• vox = 32.76

• vox = 32.8 m/s

Example 2

• In the y direction:• voy = vosin(theta)

• voy = (40.0 m/s)(sin(35 degrees))

• voy = (40.0)(0.5735)

• voy = 22.94

• voy = 22.9 m/s

Time at the top

• General:• We can use the following kinematics equation:• vf = vo + at• Subscript it for y:• vfy = voy + ayt• Solve it for t:• t = (vfy - voy) / ay

• Plug in 0.0 m/s for vfy:• t = (0.0 m/s - voy) / ay

Example• Start with:• t = (vfy - voy) / ay

• Plug in 0.0 m/s for vfy:

• t = (0.0 m/s - voy) / ay

• Plug in values for voy and ay:• t = (0.0 m/s - 22.9 m/s) / - 9.8 m/s2

• t = -22.9 / -9.8• t = 2.33• t = 2.3 s• In this example 2.3s of time passes while the projectile is

rising to the top of the trajectory.

Displacement• General:• Here is the displacement formula:• d = vot + 0.5at2

• We must think of this displacement in the y direction, so we will subscript this formula for y:

• dy = voyt + 0.5ayt2

• If now we plug in the half time of flight, which was found above, we will solve for the height of the trajectory, since the projectile is at its maximum height at this time.

Example• Starting with:• dy = voyt + 0.5ayt2

• Then plugging in known values:• dy = (22.9 m/s)(2.33 s) + (0.5)(-9.8 m/s2)(2.33

s)2

• dy = 53.35 - 26.60

• dy = 26.75

• dy = 27 m