Mechanics 9  Self Test

Print this off and answer the questions in the spaces.

For all of these questions you must use the equations of motion in:

 

a)     a vertical direction where acceleration = 9.8 m s-2 downwards

b)    a horizontal direction where acceleration = 0

 

1.     A cannonball is shot at a velocity of 100m s-1 at an angle of 30o to the horizontal.

 

a)     Calculate the initial vertical velocity. _______________________________________________________________________________ (2)

 

b)    Calculate the initial horizontal velocity. _____________________________________________________________________________ (2)

 

c)     What height will it reach? [This is when vertical velocity = 0]

 

___________________________________________________________________________________________________________(2)

 

d)    How long a time does it take to reach this maximum height?

 

__________________________________________________________________________________________________________ (2)

 

e)     If we double this time then the cannonball will have fallen back to the ground. How far in the horizontal direction has the cannonball travelled?

 

 _____________________________________________________________________________________________________________ (2)

 

 

 

 

2.     A bullet is fired at a speed of 250m s-1 at an angle of 40o to the horizontal. What will be its range? [This is the same as the above question]

 

____________________________________________________________________________________________________________

____________________________________________________________________________________________________________

____________________________________________________________________________________________________________

____________________________________________________________________________________________________________ (5)

 

 

3.     A darts player stands 2.4m away from a dartboard and throws a dart exactly horizontally. The dart hits the board 2 0cm below the level it was thrown from.

 

a)     How long did it take for the dartís flight? [Hint: For this you need to consider the vertical plane]

 

___________________________________________________________________________________________________________

____________________________________________________________________________________________________________ (2)

 

 

b)    What speed was the dart thrown at? [Hint: For this part you need to consider the horizontal plane]

 

____________________________________________________________________________________________________________

____________________________________________________________________________________________________________ (2)


 

4.     A projectile has the following conditions:

 

Initial speed = V m s-1

Angle to the horizontal = q o

Range = R

 

 

Find the range, R, in terms of an algebraic expression involving  V, q , and g.  This may seem very difficult but it is merely answering Q1 and Q2 using algebra rather than numbers.

 

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________ (5)


 

 

Extension Question

When we solve problems with projectile motion, we assume that air resistance is negligible.  How do you think the range of a projectile would be affected by air resistance?   What would the path end up as?  What factors would affect the air resistance of the projectile?

 

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

_______________________________________________________________________________________________________________

 

Answers