What are Earth's mineral resources and how long might reserves last?
1 answer:
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Answer:
v_{1fy} = - 0.4549 m / s
Explanation:
This is an exercise of conservation of the momentum, for this we must define a system formed by the two balls, so that the forces during the collision have internal and the momentum is conserved
initial. Before the crash
p₀ = m v₁₀
final. After the crash
= m
+ m v_{2f}
Recall that velocities are a vector so it has x and y components
p₀ = p_{f}
we write this equation for each axis
X axis
m v₁₀ = m v_{1fx} + m v_{2fx}
Y Axis
0 = -m v_{1fy} + m v_{2fy}
the exercise tells us the initial velocity v₁₀ = 1.83 m / s, the final velocity v_{2f} = 1.15, let's use trigonometry to find its components
sin 23.3 = v_{2fy} / v_{2f}
cos 23.3 = v_{2fx} / v_{2f}
v_{2fy} = v_{2f} sin 23.3
v_{2fx} = v_{2f} cos 23.3
we substitute in the momentum conservation equation
m v₁₀ = m v_{1f} cos θ + m v_{2f} cos 23.3
0 = - m v_{1f} sin θ + m v_{2f} sin 23.3
1.83 = v_{1f} cos θ + 1.15 cos 23.3
0 = - v_{1f} sin θ + 1.15 sin 23.3
1.83 = v_{1f} cos θ + 1.0562
0 = - v_{1f} sin θ + 0.4549
v_{1f} sin θ = 0.4549
v_{1f} cos θ = -0.7738
we divide these two equations
tan θ = - 0.5878
θ = tan-1 (-0.5878)
θ = -30.45º
we substitute in one of the two and find the final velocity of the incident ball
v_{1f} cos (-30.45) = - 0.7738
v_{1f} = -0.7738 / cos 30.45
v_{1f} = -0.8976 m / s
the component and this speed is
v_{1fy} = v1f sin θ
v_{1fy} = 0.8976 sin (30.45)
v_{1fy} = - 0.4549 m / s
Answer:
7.5 meters per second
Explanation:
30 / 4 = 7.5
7.5 * 1 = 7.5
7.5 * 2 = 15
7.5 * 3 = 22.5
7.5 * 4 = 30
Answer:
Explanation:
Let v is the launch speed of the plastic ball and the angle of projection is θ.
So, in horizontal direction
v Cosθ x t = 4.8 .... (1)
In th evertical direction
1.4 = v Sin θ x t - 0.5 gt² .... (2)
As , v Sin θ x t = 3.8 .... (3) , put in equation (2)
1.4 = 3.8 - 4.9 t²
t = 0.7 s
Put in (1) and (3)
v Cosθ x 0.7 = 4.8
v Cosθ = 6.86
and v Sinθ x 0.7 = 3.8
v Sinθ = 5.43
Now
v = 8.75 m/s