How High is the Cliff in the Pocahontas Cartoon Movie?
a) What is the height of the cliff if Pocahontas runs at 3.0 m/s before jumping off?
a) (i) 19.94m
b) How fast would Pocahontas be falling right before hitting the water if she jumped off the cliff from a standstill?
b) (i) 19.76m/s
a) Answer:
In the Pocahontas cartoon movie, when Pocahontas runs at 3.0 m/s before jumping off the cliff, the height of the cliff is calculated to be 19.94m. This is determined using the conservation of energy principle, where the initial kinetic energy and potential energy equal the final kinetic energy gained and potential energy as she falls. The height of the cliff is determined to be 19.94m when Pocahontas runs at 3.0 m/s before jumping off.
b) Answer:
If Pocahontas were to jump off the same cliff from a standstill, she would be falling right before hitting the water at a speed of 19.76m/s. This is calculated by considering the initial velocity as 0 and applying the conservation of energy principle. The final velocity before hitting the water is determined to be 19.76m/s.
The calculation of the height of the cliff in the Pocahontas cartoon movie involves applying the principles of conservation of energy. In the scenario where Pocahontas runs at 3.0 m/s before jumping off, the initial kinetic energy and potential energy are equal to the final kinetic energy gained and potential energy as she falls.
By utilizing the equation for conservation of energy, the height of the cliff can be determined. The kinetic energy (KE) is calculated using the formula KE = 1/2 * m * u^2, and the potential energy (PE) is represented as PE = m * g * h, where h is the height of the cliff.
Therefore, the equation becomes: 1/2 * (m) * (3.0 m/s)^2 + m * (9.8 m/s^2) * h = 1/2 * m * (20 m/s)^2. By solving for h, the height of the cliff is calculated to be 19.94m when Pocahontas runs at 3.0 m/s before jumping off.
On the other hand, if Pocahontas were to jump off the cliff from a standstill, her initial velocity would be 0. By applying the conservation of energy principle again, the final velocity before hitting the water is determined to be 19.76m/s.