Consider a system of two particles in the xy plane: m 1 = 2.00 kg is at the location r → 1 = ( 1.00 i ^ + 2.00 j ^ ) m and has a velocity of ( 3.00 i ^ + 0.500 j ^ ) m / s ; m 2 = 3.00 kg is at r → 2 = ( − 4.00 i ^ + 3.00 j ^ ) m and has velocity ( 3.00 i ^ + 2.00 j ^ ) m / s . (a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (b) Find the position of the center of mass of the system and mark it on the grid. (c) Determine the velocity of the center of mass and also show it on the diagram. (d) What is the total linear momentum of the system?
Consider a system of two particles in the xy plane: m 1 = 2.00 kg is at the location r → 1 = ( 1.00 i ^ + 2.00 j ^ ) m and has a velocity of ( 3.00 i ^ + 0.500 j ^ ) m / s ; m 2 = 3.00 kg is at r → 2 = ( − 4.00 i ^ + 3.00 j ^ ) m and has velocity ( 3.00 i ^ + 2.00 j ^ ) m / s . (a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (b) Find the position of the center of mass of the system and mark it on the grid. (c) Determine the velocity of the center of mass and also show it on the diagram. (d) What is the total linear momentum of the system?
Solution Summary: The author illustrates the position and velocity vectors of the two particles in x-y plane.
Consider a system of two particles in the xy plane: m1 = 2.00 kg is at the location
r
→
1
=
(
1.00
i
^
+
2.00
j
^
)
m
and has a velocity of
(
3.00
i
^
+
0.500
j
^
)
m
/
s
; m2 = 3.00 kg is at
r
→
2
=
(
−
4.00
i
^
+
3.00
j
^
)
m
and has velocity
(
3.00
i
^
+
2.00
j
^
)
m
/
s
. (a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (b) Find the position of the center of mass of the system and mark it on the grid. (c) Determine the velocity of the center of mass and also show it on the diagram. (d) What is the total linear momentum of the system?
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
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