A small dog is trained to jump straight up a distance of 1.2 m. How much kinetic energy does the 7.2-kg dog need to jump this high? (The acceleration due to gravity is 9.8 m/s2.) Show your work.
A. 85 J
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To find the kinetic energy, we need to use the formula: Kinetic Energy (KE) = 1/2 * mass * velocity^2.
However, we are not given the velocity directly, so we need to find it.
To solve this, we will use the concept of gravitational potential energy. The dog's potential energy at the highest point is equal to the kinetic energy when it jumps off the ground.
The formula for potential energy is: Potential Energy (PE) = mass * acceleration due to gravity * height.
In this case, the height is 1.2 m and the acceleration due to gravity is 9.8 m/s^2. We know the mass of the dog is 7.2 kg, so we can calculate the potential energy.
PE = 7.2 kg * 9.8 m/s^2 * 1.2 m
PE = 84.096 joules
Since the potential energy is equal to the kinetic energy at the highest point, we can equate them:
KE = PE
KE = 84.096 joules
Therefore, the kinetic energy required for the dog to jump this high is 84.096 joules.