Kinematics/Newton's Laws - The Burns Home Page

9/3/2009
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
(a) Show that the cannonball will strike the wall.
(b) How long will it take for the cannonball to strike the wall?
(c) At what height above the base of the wall will the cannonball strike?
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
(a) Show that the cannonball will strike the wall.
1 2
x v0
xt
y v0
yt gt
2
x
2
t
x 1 x
v
v0
sin
2
0x
g
v0cos
2 v0cos
x
2
gx
v cos x tan
2 2
0
2v0
cos
m
2
9.8 2 220m
s
220m tan 40
2
m 2
250 cos 40
s
23m
v 2
sin 0 2
R
g
m
50 sin 240
s
R
m
9.8
2
s
251m
We need now only show that the
height of the ball is below 30 m
when the horizontal displacement
is 220m
This is less than 30 m, so contact
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
b) How long will it take for the cannonball to strike the wall?
x
t
v
0x
x
v cos 0
220m
m
50 cos40
s
5.7s
Understanding
A cannonball is shot with an initial speed of 50 m/s at a launch angle of 40 0
toward a castle wall 220m away. The height of the wall is 30 m. Assume that
effects due to the air are negligible.
c) At what height above the base of the wall will the cannonball strike?
From (a) we have 23 m
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