Miss E. deWater, the former platform diver of the Ringling Brothers' Circus, dives from a 80.0-meter high platform into a shallow bucket of water (see diagram at right). Determine her speed and her height after each second of fall.
When t = 0 s: speed = 0 m/s and height = 80 m
Should I use kinematic equations to find acceleration then plug that in?
yes
at each second
v = previous v + 9.81
Distance down = previous distance down + previous v + 4.9
Distance down = previous distance down + previous v * 4.9
Distance down = previous distance down + previous v * 1 + 4.9 * 1^2
Yes, you can use kinematic equations to find the acceleration and then use that information to determine Miss E. deWater's speed and height after each second of the fall.
To start, you can use the equation for the acceleration of an object in free fall near the surface of the Earth, which is approximately 9.8 m/s². Since Miss E. deWater is diving into a shallow bucket of water, air resistance may have some effect, but we will assume it is negligible for simplicity.
Using the equation of motion "v = u + at", where:
- v is the final velocity (speed) of the object,
- u is the initial velocity (speed),
- a is the acceleration of the object, and
- t is the time taken,
we can find the speed and height after each second of the fall.
First, we calculate the speed at each second by adding the acceleration at each second.
For t = 0 s:
- Speed: v = u + at = 0 + (9.8 × 0) = 0 m/s
- Height: Since the speed is 0, the height remains at 80 m.
For t = 1 s:
- Speed: v = u + at = 0 + (9.8 × 1) = 9.8 m/s
- Height: We can use the equation for displacement (h = ut + 0.5at²) to find the change in height from t = 0 s to t = 1 s:
h = (0 × 1) + (0.5 × 9.8 × 1²) = 4.9 m
Therefore, the height at t = 1 s is 80 m - 4.9 m = 75.1 m
You can continue this process to find the speed and height after each subsequent second of the fall.