Projectile motion.

**simonbailyes** · July 15th 2010, 06:08 AM

A cannonball was shot out of a tower.

The cannonball left the window at a horizontal speed of 20 metres per second, and the window was at a height of 45 metres, and the ground outside of the tower was perfectly horizontal, and the cannonball's mass was 6.2 kg. Assume gravitational acceleration of 9.8 metres per second squared.
How much horizontal distance will the cannonball travel from the tower before hitting the ground?

This problem has been bugging me for a while. There are no additional forces. Could someone explain how to get the answer please?

Thanks,
Simon

**Soroban** · July 15th 2010, 07:41 AM

Hello, simonbailyes!

A cannonball was shot out of a tower.
The cannonball left the window at a horizontal speed of 20 m/s.
The window was at a height of 45 metres.
The ground outside of the tower was perfectly horizontal.
The cannonball's mass was 6.2 kg.
Assume gravitational acceleration of 9.8 $m/s^2$ .

What horizontal distance will the cannonball travel from the tower
before hitting the ground?

You are expected to apply the "trajectory functions" and get:

. . Vertical position: . $y \;=\;45 - 4.9t^2$

. . Horizontal position: . $x \;=\;20t$

The cannon ball hits the ground when $y \,=\,0$

. . $45 - 4.9t^2 \:=\:0 \quad\Rightarrow\quad t^2 \:=\:\dfrac{45}{4.9} \quad\Rightarrow\quad t \:=\:\dfrac{15\sqrt{2}}{7}\text{ seconds}$

In that time, the cannonball travels a horizontal distance of:

. . $x \;=\;20\left(\dfrac{15\sqrt{2}}{7}\right) \;=\;\dfrac{300\sqrt{2}}{7} \;\approx\;60.6\text{ meters}$

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