Problem 7: A man with an egg-shaped-head presses straight down (negative y-direction) on a tabletop at a constant speed of 2 m/sec. This creates the table to rotate counterclockwise at a constant angular speed of 5 rad/sec. Relative to the moving coordinate system of the tank, the fish swims at a speed of 6 m/sec purely in the x' direction, and it has a magnitude of acceleration of 0.5 m/sec² directed purely in the y' direction. Note that the origin O is a stationary point. 1.5 m 20° x 0.7 m 15" (Oi 05)rad/sec Figure 6: Fish tank being launched off table. = (07 +07 - 2k) rad/sec (0 0 1) rad/sec² 0.1 m i) ii) What is the velocity of the point O'relative to the stationary coordinate system? What is the acceleration of the point O'relative to the stationary coordinate system? iii) iv) What is the velocity of the fish relative to the stationary coordinate system? What is the acceleration of the fish relative to the stationary coordinate system?
Problem 7: A man with an egg-shaped-head presses straight down (negative y-direction) on a tabletop at a constant speed of 2 m/sec. This creates the table to rotate counterclockwise at a constant angular speed of 5 rad/sec. Relative to the moving coordinate system of the tank, the fish swims at a speed of 6 m/sec purely in the x' direction, and it has a magnitude of acceleration of 0.5 m/sec² directed purely in the y' direction. Note that the origin O is a stationary point. 1.5 m 20° x 0.7 m 15" (Oi 05)rad/sec Figure 6: Fish tank being launched off table. = (07 +07 - 2k) rad/sec (0 0 1) rad/sec² 0.1 m i) ii) What is the velocity of the point O'relative to the stationary coordinate system? What is the acceleration of the point O'relative to the stationary coordinate system? iii) iv) What is the velocity of the fish relative to the stationary coordinate system? What is the acceleration of the fish relative to the stationary coordinate system?
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Please show all steps. Use a format of " v_p/O' " to represent velocity of point 'p' with respect to the rotated origin, or something of that manner.
Transcribed Image Text:Problem 7: A man with an egg-shaped-head presses straight down (negative y-direction) on a
tabletop at a constant speed of 2 m/sec. This creates the table to rotate counterclockwise at a
constant angular speed of 5 rad/sec. Relative to the moving coordinate system of the tank, the
fish swims at a speed of 6 m/sec purely in the x' direction, and it has a magnitude of acceleration
of 0.5 m/sec² directed purely in the y' direction. Note that the origin O is a stationary point.
1.5 m
20°
x
0.7 m
15"
(Oi 05)rad/sec
Figure 6: Fish tank being launched off table.
= (07 +07 - 2k) rad/sec
(0 0 1) rad/sec²
0.1 m
i)
ii)
What is the velocity of the point O'relative to the stationary coordinate system?
What is the acceleration of the point O'relative to the stationary coordinate system?
iii)
iv)
What is the velocity of the fish relative to the stationary coordinate system?
What is the acceleration of the fish relative to the stationary coordinate system?
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