Answer:
39.7 m/s
Explanation:
The motion of the cannonball consists of a horizontal and a vertical motion. The vertical motion is under gravity while the horizontal motion is a constant-velocity motion. Both motions span the same time interval. We consider them differently.
Vertical motion:
Acceleration, [tex]a=9.80[/tex]
Initial velocity, [tex]u=0.00[/tex] (since the ball was fired horizontally)
Distance, [tex]s=70.0[/tex]
Using the equation [tex]s=ut+\frac{1}{2}at^2[/tex],
[tex]70.0=0+\frac{1}{2}9.80t^2[/tex]
[tex]t=\sqrt{\dfrac{70.0}{4.90}}=\dfrac{10.0}{\sqrt{7}} [/tex]
Horizontal motion:
Since there is no acceleration, horizontal velocity = horizontal distance ÷ time for vertical motion.
[tex]v=\dfrac{d}{t}[/tex]
[tex]v=\dfrac{150}{\frac{10.0}{\sqrt{7}}}[/tex]
[tex]v=15\sqrt{7}=39.7[/tex]
