The tomato is dropped. What is the velocity, v, of the tomato when it hits the ground? Assume 94.7% of the work done in Part A is transferred to kinetic energy, E, by the time the tomato hits the ground.
something vital is missing here.
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To determine the velocity of the tomato when it hits the ground, we need some additional information. Specifically, we need to know the initial height from which the tomato is dropped, as well as any other relevant variables such as the acceleration due to gravity.
Once we have these values, we can proceed with calculating the velocity at impact using the principle of conservation of energy. According to the information given, 94.7% of the work done is transferred to kinetic energy by the time the tomato hits the ground.
Can you please provide the missing information, such as the initial height and any other relevant variables?
To determine the velocity of the tomato when it hits the ground, we can use the principles of energy conservation and the work-energy theorem.
First, we need to know the height from which the tomato was dropped and the work done in Part A. Let's assume the height is denoted as 'h' and the work done as 'W'.
Since it is mentioned that 94.7% of the work is transferred to kinetic energy, we can calculate the amount of work that got converted into kinetic energy. Let's denote this as 'W_kinetic'.
W_kinetic = 0.947 * W
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy:
W = ΔKE
At the topmost point of its trajectory, the tomato has zero kinetic energy (since it is at rest). When it reaches the ground, it will have a certain amount of kinetic energy.
ΔKE = KE_final - KE_initial
The initial kinetic energy (KE_initial) is zero, and the final kinetic energy (KE_final) is given by:
KE_final = W_kinetic
Substituting the values, we get:
ΔKE = W_kinetic - 0 = W_kinetic
Now, the change in kinetic energy is also equal to the work done by gravity, which can be calculated using the formula:
ΔKE = m * g * h
where 'm' is the mass of the tomato, 'g' is the acceleration due to gravity (approximately 9.8 m/s^2), and 'h' is the height from which the tomato was dropped.
Setting the two expressions for change in kinetic energy equal to each other, we have:
W_kinetic = m * g * h
Finally, we can rearrange the equation to solve for velocity 'v':
v = √(2 * (W_kinetic / m))
By substituting the values of 'W_kinetic' and assuming a specific mass, you can calculate the velocity 'v' of the tomato when it hits the ground.