An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C. Both rods have the
1 answer:
Response:
0.9 cm
Clarification:
The following illustrates the calculation of the combined rod's length increase:
As established
Length increase = expansion of aluminum rod + expansion of steel rod
= 0.9 cm
We simply summed the expansions of both the aluminum and steel rods to determine the overall increase in the joined rod's length, which must be factored in
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Explanation:
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Answer:
The BMX rider lands 5.4 meters horizontally away from the ramp's end.
Explanation:
The BMX position vector is represented as:
r = (x0 + v0 × t × cos α, y0 + v0 × t × sin α + ½ × g × t²)
Where:
r = position at time t
x0 = initial horizontal position
v0 = initial speed
α = angle of jump
y0 = initial vertical height
g = gravitational acceleration (-9.8 m/s², upward positive)
Refer to the diagram for clarity. At the landing time, the vertical coordinate of the position vector is -2.4 m, measured from the ramp's edge as the origin. Using the vertical component equation for y, one can solve for t, then substitute t to find the horizontal distance.
The vertical position equation:
-2.4 m = 0 + 5.9 m/s × t × sin 40° - ½ × 9.8 m/s² × t²
Rearranged:
0 = -4.9 t² + 5.9 t × sin 40° + 2.4
Solving this quadratic yields:
t = 1.2 seconds
Then, calculate horizontal distance:
x = 0 + 5.9 m/s × 1.2 s × cos 40° = 5.4 m
This means the BMX lands 5.4 meters from the ramp's edge.
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