Projectile Motion

The Trajectory

plotting the parabola

Reading the across and up positions at each second and plotting the points traces the curved path of a thrown ball.

Example

Reading the across and up positions at each second and plotting the points traces the familiar curved path of a thrown ball.

highlighted = computed this step

Track both parts each second

We already have across position equal to 5 times time, and up position equal to 10 times time minus 5 times time squared. Now read both at each second.

x=5 m/s t,y=10 m/s t−5 t2x = 5\ \text{m}/\text{s}\,t, \quad y = 10\ \text{m}/\text{s}\,t - 5\,t^{2}

After one second

At one second the ball has moved across to 5 and risen to 5 metres. It is still climbing.

(x,y)=(5,5)(x, y) = (5, 5)

After two seconds

At two seconds it has coasted across to 10 and fallen back to the ground at height 0. Plotting the points traces a parabola.

(x,y)=(10,0)(x, y) = (\hl{10}, \hl{0})
The path curves: a parabolaThe ball sampled every half second, rising then falling along a curved path back to the ground.t=0t=1ball
mechanics With clean components and g = 10, the second-by-second positions are whole numbers that fall on a parabola.