Projectile motion Vectors and scalars A scalar quantity is described only by its magnitude Examples – 5.0kg; 10.0 l; 50.0 o C; 10.0m/s

Projectile motion Vectors and scalars A vector quantity is described by its magnitude and by its direction. Examples – 10.0 m/s north; 10.0m/s 2 down; 5.0N up.

Projectile motion Vectors and scalars Vector quantities are represented by arrows. The length of the arrow is proportional to the magnitude of the vector quantity. The head of the arrow points in the direction of the vector. The other end of the arrow is the tail of the vector.

Two vectors

Projectile motion When vectors are parallel to each other we add and subtract them in a straightforward manner. If they have the same sign (point in the same direction) we add their magnitudes.

Projectile motion. If they have different signs (point in the opposite directions), we subtract their magnitudes.

Parallel vectors – page 39

Two vectors – tail to tail

Projectile motion Vectors and scalars We can add vectors by putting their tails together, and drawing dotted lines parallel to the vectors.

Two vectors with parallel lines

Projectile motion Vectors and scalars We draw a diagonal from the point where the two tails meet to the opposite corner of the rectangle that was formed.

Projectile motion Vectors and scalars The diagonal is the sum of the two original vectors and is called the resultant.

Projectile motion

Airplane flying in crosswind (page30)

Projectile motion Frequently it is convenient to separate vectors into perpendicular components. We do this by constructing a parallelogram that has the vector as a diagonal.

Separating a vector into components.- page 32

A velocity vector resolved into components – page 32

Projectile motion A projectile is an object moving only under the influence of gravity. We also say that the object is in free fall. We can separate the horizontal and vertical components of a projectile’s velocity by using vectors.

Projectile motion The horizontal component of a projectile’s velocity does not change. It is constant.

Projectile motion The vertical component of a projectile’s velocity is always changing because it always accelerating downward.

Projectile motion The two motions can be treated independently.

Projectile motion Demonstration.

Projectile motion

If a projectile is launched upward at an angle, it will follow a parabolic path if there is no air resistance.

Projectile motion

In the presence of air resistance the parabolic path is altered.

Projectile motion

Satellites are projectiles that move so fast, that the Earth curves away from them at the same rate that they are falling toward the earth. This can only happen beyond the atmosphere where an object moving at those speeds will not burn up fron air friction.

Projectile motion