What was the cannonball's final speed when it hit the soldier?

Question

If a cannonball was shot off 20 meters away from a soldier, and it's acceleration was 5m/s^2. What was the cannonball's final speed when it hit the soldier?

 

Hint: The Initial speed was 0m/s.

 

Show work please, thank you.

Answer 1

We do not know how long is the barrel of the cannon, or what time it traveled through the barrel. But this should not prevent us from finding a solution.

Assume that the distance it traveled through the barrel of the cannon = d1

and the distance it traveled through air = d2

The total distance traveled by the cannonball = d1 + d2 = 20 m

 

                    In Barrel (a = 5m/s^2)                In Air (5 seconds)

       0 m/s-------------------------------------- v---------------------------v (hits soldier)

                         d1                                               d2 = 5 v

 

Using the equations of motion to find d1 and d2,

v^2 = 0 ^2 + 2 (5) d1              d1 = v^2 /10                   d2 = 5 v

 

d1 + d2 = 20 meters          v^2 /10 + 5 v = 20          v^2  + 50 v = 200

 

v^2 + 50 v - 200 = 0

Solve this equation using the quadratic formula to obtain  v = 3.72 m/s

    

 

Answer 2

Use the equation

V^2 = u^2 + 2 as

 

V is the final velocity we need to find

 

V^2 = 0^2 + 2 * 5 * 20

 

V = sqrt 200

 

=  14.142 m/s