1 U6 2D Motion - ws 4 v3.1
Name
Date Pd
Particle Motion in Two Dimensions Model Worksheet 4:
Projectile Motion Problems
1. A metal sphere is launched with an initial velocity of 1.5 m/s as it leaves the ramp. The end
of the ramp is 1.20 m above the floor. Calculate the range of the sphere. (Range is the
horizontal displacement of the projectile.)
cos20 (1.5 ) 1.4
sin20 (1.5 ) 0.51
mm
xss
mm
yi ss
v
v
2
2
22
11
22
2(use solver or quadratic)
-1.2m=(0.51 )t ( 10 )
( 5 ) (0.51 )t 1.2m 0 0.54
1.4 (0.54 ) 0.76
mm
yi ss
mm
s
s
m
xs
y v t a t t
t t s
x v t x s m
2. Now the ramp is tilted downwards and the sphere leaves the ramp at 1.5 m/s as shown below.
The bottom of the ramp is 0.90 m above the floor. Calculate the range of the sphere.
cos15 (1.5 ) 1.45
sin20 (1.5 ) 0.51
mm
xss
mm
yi ss
v
v
2
2
22
11
22
2(use solver or quadratic)
-0.90m=(-0.51 )t ( 10 )
( 5 ) (-0.51 )t 0.90m 0 0.37
1.45 (0.37 ) 0.54
mm
yi ss
mm
s
s
m
xs
y v t a t t
t t s
x v t x s m
1.2 m
y = -1.2 m
vyi = 0.51
m
s
a = g = -10
2
m
s
vx = 1.4
m
s
t = ?
x = ?
y
x
vx
vyi
v = 1.5
m
s
20°
y = -0.90 m
vyi = -0.51
m
s
a = g = -10
2
m
s
vx = 1.45
m
s
t = ?
x = ?
0.90 m
y
x
vx
vyi
v = 1.5
m
s
15°
