On a coordinate plane, vertex A for triangle ABC is located at (6,4). Triangle ABC is dilated by a scale factor of 0.5 with the
1 answer:
<h2>Answer:</h2>
Dilation is when you stretch something by the same amount in two perpendicular directions. In other words, dilation changes size, not overall shape. If the factor of dilation is greater than one the shape is greater than the original, else if the scale factor is less than one the shape is smaller. In this problem, we must find the coordinates of A'. Since the center of dilation is the origins, we just need to multiply the coordinates of A by 0.5. So:
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Answer:
(a) x = 0.25 m
(b) v = 1.46 m/s
(c) v = 2.4 m/s
Explanation:
mass (m) = 10.3 kg
force from thrust (F) = 240 N
spring constant (k) = 400 N/m
stretch distance from thrust (y) = 30 cm = 0.3 m
acceleration due to gravity (g) = 9.8 m/s^{2}
(A) from mg = kx
compression (x) = mg/ k
x =
x = 0.25 m
(B) from the conservation of forces
(Fy) + (0.5k) = (0.5k
) + mgh + (0.5m
)
v = ) - (0.5k
) - mgh }{0.5m}[/tex]}[/tex]
v = ) - (0.5 x 400 x
) - (10.3 x 9.8 x (0.25 + 0.3)) }{0.5 x 10.3}[/tex]}[/tex]
v = 1.46 m/s
(C) if the rocket weren't attached to the spring, the conservation of energy equation becomes
(Fy) + (0.5k) = mgh + (0.5m
)
v = ) - mgh }{0.5m}[/tex]}[/tex]
v = ) - (10.3 x 9.8 x (0.25 + 0.3)) }{0.5 x 10.3}[/tex]}[/tex]
v = 2.4 m/s