1.1 PROJECTLE MOTION

Vectors and Scalars Scalar:a quantity that has only magnitude (size) but not direction e.g. mass, time, speed, distance Vector:a quantity that has both magnitude and direction e.g. velocity, displacement, acceleration

Vectors and Scalars

A A B B Distance (path taken) = 15 m Displacement = 10 m North East Distance and Displacement

A A B B Horizontal displacement = 5 cm right Vertical displacement = 0 cm

Vector Components

Parabolic Path

HorizontalVertical Projectile Motion

Multi-Image Photographs

Assume 0.01 s between each photo. Show that the horizontal component of velocity is constant and calculate its value. Example 1

Projectile Motion Calculations

Equations of MotionOmitted Quantity Projectile Motion Calculations vertical values horizontal values

A mortar shell is fired from ground level with a velocity of 100 m.s -1 at 80 ° above the horizontal. Find: a)the initial horizontal and vertical components of velocity b)the vertical component of velocity 13 s after firing c)the magnitude and direction of the velocity of the mortar shell after 13 s d)the magnitude and direction of the velocity of the shell at the top of its flight e)the maximum height reached by the shell f)the shell's time of flight g)the range of the shell Example 2

A parcel is dropped from a plane into the sea. The plane is flying at 100 m.s -1 horizontally at 120 m above sea level. Find: a)the vertical distance fallen by the parcel after 2 s b)the vertical component of velocity of the parcel after 2 s c)the magnitude and direction of the velocity of the parcel after 2 s d)how long the parcel takes to hit the water Example 3

You throw a baseball 42.8 m and it spends 1.64 s in the air. Calculate the magnitude and direction of the ball’s final velocity just before it is caught (assuming it is caught at the same height as it was thrown). Hence, state its initial velocity m Example 4

1) An aeroplane is to drop a parcel of medical supplies to a boat in the sea. The aeroplane is flying horizontally at a height of 240 m above sea level with a speed of 90ms-1. Calculate : a) the time between the parcel leaving the aeroplane and hitting the water. ( ie the time of flight) How far from the boat the aeroplane must release the parcel ( ie the range of the projectile. The velocity of the parcel on hitting the water. Practice

A cricketer, fielding in the outfield, throws a ball to the wicket keeper, with a speed of 23ms-1 at an angle of 30 deg above the horizontal. The wicket keeper catches the ball at the same level at which it was originally thrown. Find : The time of flight of the ball The distance of the fielder from the wicket keeper (range) The velocity with which the ball strikes the wicket keeper’s gloves. Practice

3) A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table's edge and the ball's landing location. Practice

4) A soccer ball is kicked horizontally off a meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball. Practice

The Effect of Launch Angle on Range

The Effect of Air Resistance

Air resistance acts in the opposite direction to the object’s motion. This force depends on the object’s:  size – the larger the size, the greater the resistance since more air particles contact its surface increasing friction.  shape and surface texture – these affect how easy it is for air particles to move around the object.  speed – the faster the speed, the greater the resistance.

The Effect of Air Resistance No air resistance Air resistance

Application: Projectiles in Sport

Horizontal displacement greater launch height has further to fall Application: Projectiles in Sport A larger launch height gives a larger range.

Application: Projectiles in Sport B A