**I. Motion of a projectile**

The velocity vector changes in both magnitude and direction.

A. Let **v _{0}** be the initial velocity and q

**v _{0} = **v

v_{0x} = v_{0}cosq _{0} and v_{0y} = v_{0}sinq _{0}

B. Use vector equations: **v** = **v _{0} + a**t and

1.Use components:

v_{x} = v_{0x} + a_{x}t and x - x_{0 }= v_{0x}t + (1/2)a_{x} t^{2}

v_{y} = v_{0y} + a_{y}t and y - y_{0 }= v_{0y}t + (1/2)a_{y} t^{2}

C. For projectile motion:

1.a_{x} = 0

2. a_{y} = -g = -9.8 m/s^{2 }= -32 f/ s^{2}

3. v_{x} = v_{0}cosq _{0 }

4. v_{y} = v_{0}sinq _{0 }-gt

5. Then: v^{2} = v_{x}^{2} + v_{y}^{2} and tanq = v_{y}/v_{x}

where q is the angle that the velocity vector makes with the horizontal at *any time* and v is the magnitude of the velocity vector at *any time*.

D. The projectile's coordinates, assuming that it starts from the origin are:

1. x = v_{0x}t = (v_{0}cosq _{0})t

2. y = (v_{0}sinq _{0})t - (1/2)gt^{2}_{ }

Example

A soccer player kicks a ball at an angle of 37 degrees from the horizontal with an initial speed of 20 m/s.

a) Find the time to reach the highest point of the trajectory, T.

b) How high does the ball go?

c) What is the horizontal range of the ball?

d) How long is it in the air?

e) What is the VELOCITY of the ball when it strikes the ground?