Projectile Motion

Time of Flight and Range

when and where it lands

Because the across speed is constant, once we know how long the ball is in the air the distance falls right out.

Example

Because the across speed is constant, once we know how long the ball is in the air the distance it travels falls right out.

highlighted = computed this step

When does it land?

It lands when the height is back to zero. The up part climbs and falls symmetrically, so it lands after twice the time to the top. Gravity erases the 10 metres per second of upward speed at 10 per second, reaching the top at one second and landing at 2 seconds.

tland=2vyg=2 ⋅ 10 m/s10 m/s2=2 st_{\text{land}} = \frac{2 v_y}{g} = \frac{2\,\cdot\,10\ \text{m}/\text{s}}{10\ \text{m}/\text{s}^{2}} = \hl{2}\ \text{s}

How far does it go?

The across speed never changed, so the range is just 5 metres per second times the 2 seconds of flight: 10 metres.

x=vx tland=5 m/s ⋅ 2=10 mx = v_x\,t_{\text{land}} = 5\ \text{m}/\text{s}\,\cdot\,2 = \hl{10}\ \text{m}
Where it landsThe ball's arc from the launch point back down to its landing spot on the ground, with the landing point marked.starttopland
mechanics Symmetric up-and-down flight with clean numbers lands at a whole second, so the range is exact.