1) The document describes the motion of a projectile under constant acceleration due to gravity. It gives equations for the position r, velocity v, and components x and y over time. 2) Additional equations are derived for the projectile's motion when it is launched at an angle α to the horizontal. The velocity components vx and vy are expressed in terms of the launch speed v0 and angle α. 3) The trajectory of the projectile is shown to be parabolic, with the equation y = y0 - (g*t^2)/(2v0x) relating the y position to the launch conditions and time.

1. 1 2
r = r0 + v0t + at = xi + yj
2
v = v0 + at = vx i + v y j
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2. 1 2 3
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1 2
r = yj = r0 + v0t + a t = y0 j − 5t 2 j y = y 0 − 5t 2
2
v = v y j = v0 + at = −10tj v y = − 10 t
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1 2
r = yj = r0 + v0t + a t = y0 j + v0 y tj − 5t 2 j
2
y = y 0 + v 0 y t − 5t 2
v = v y j = v0 + at = v0 y j − 10tj v y = v 0 y − 10 t

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1 2
r = xi + yj = r0 + v0t + at = y0 j + v0 xti − 5t 2 j
2
x = v0 x t y = y 0 − 5t 2
v = v x i + v y j = v0 + at = v0 x i − 10tj
v x = v 0 x = cte v y = − 10 t
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y = y0 − 2
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4. 2
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v0 x = v0 ⋅ cos α v0 y = v0 ⋅ senα
1 2
r = xi + yj = r0 + v0t + a t = y0 j + v0 xti + v0 y tj − 5t 2 j
2
x = v0 x t y = y 0 + v 0 y t − 5t 2
v = v x i + v y j = v0 + at = v0 x i + v0 y j − 10tj
v x = v 0 x = cte v y = v 0 y − 10 t
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