Department of Physics, The Chinese University of Hong Kong
Copyright © 2003 Education and Manpower Bureau, HKSAR
Activity: How high can a dolphin 'jump'?
Key Learning Points:
- Speed and velocity
- Vertical motion under gravity
- Motion graphs
Introduction
Students will look at the motion of the dolphins at Ocean Theatre. They will take a video of a dolphin which performs a 'jump' to reach a hanging ball. From the data obtained from the video, they can estimate the vertical acceleration of the dolphin and the height of the ball above water level. Motion Video Analysis can be used to obtain a s-t graph and a better value of the acceleration.
Background knowledge
Vertical motion under gravity
Equation of uniformly accelerated motion
Motion graphs of uniformly accelerated motion
Procedure
A dolphin jumping up to reach a ball.
Take a video of a dolphin which performs a 'jump' to reach a hanging ball.
From the digitized video, find the time required for the dolphin to perform this action.
Estimate the maximum height of the dolphinabove water by using the equation of motion under gravity. Compare the result with the height of the ball provided by Ocean Park.
Use the Video Motion Analysis Software to plot a s-t graph of the dolphin. Use the height of the ball provided by Ocean Park as the reference length.
Export the motion data to a file. Fit the data with a quadratic curve by using a spreadsheet such as MS Excel. Obtain the acceleration of the dolphin from the equation of the best-fitted curve.
You may also try to do a similar experiment with the sea lions.
Discussion
How do you calculate the height of the ball by using the equation of motion under gravity? Which part of the dolphin's motion can be chosen to do the calculation?
How is the calculated height of the dolphin compared with the given height of the ball? What causes the difference?
How is the acceleration found compared with the acceleration due to gravity? What causes the difference?
Have you done a similar experiment with the sea lions? The height that a sea lion can reach is much less than that of a dolphin, how would this affect the result?
The dolphin has a length not small compared with the height of the ball. When the dolphin begins to 'jump' up, part of it is still in water. How would this affect the results?
During the 'jump', the dolphin may also swing its tail and turn its body. How would this affect the results? How about the sea lion?
What are the other sources of uncertainties in this experiment?
Teachers' Notes
Typical Result
Height of the ball above water = 3.96 m (provided by Ocean Park)
Acceleration = 2 4.84 ms-2 = 9.7 ms-2
Height of the ball above water = 2.29 m (provided by Ocean Park)
Acceleration = 2 4.06 ms-2 = 8.1 ms-2
Estimating the maximum height of the jump
Let's consider the dolphin's upward motion.
Time for the upward motion = 0.83 s
Since
Time for the upward motion = Time for the downward motion
Applying to the downward motion, we have
This is about 15% smaller than the given height of the ball. The above calculation actually gives the maximum height of the dolphin's centre of mass above water, which is expected to be smaller than the height of the ball.
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