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 for credit.
e = m g h = 7.2 * 9.8 * 1.2 (Joules)
how does that give you ke
the ke at the bottom equals the pe at the top
both measured in Joules
To calculate the kinetic energy needed for the small dog to jump, we can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
However, we first need to calculate the initial velocity the dog needs to jump to a height of 1.2 m.
Working with the equation of motion for vertical motion under the force of gravity:
Final Velocity^2 = Initial Velocity^2 + 2 * acceleration * displacement,
where:
Initial Velocity = 0 (assuming the dog starts from rest)
Final Velocity = ?
Acceleration = acceleration due to gravity = 9.8 m/s^2
Displacement = height = 1.2 m
Rearranging the equation, we have:
Final Velocity^2 = 0^2 + 2 * 9.8 m/s^2 * 1.2 m
Final Velocity^2 = 2 * 9.8 m/s^2 * 1.2 m
Final Velocity^2 = 23.52 m^2/s^2
To find the Final Velocity, we take the square root of both sides:
Final Velocity = √ (23.52 m^2/s^2)
Final Velocity ≈ 4.85 m/s (rounded to two decimal places)
Now that we have the Final Velocity, we can calculate the Kinetic Energy using the given mass of the dog:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 7.2 kg * (4.85 m/s)^2
Kinetic Energy = (1/2) * 7.2 kg * 23.5225 m^2/s^2
Kinetic Energy = 83.985 J (rounded to three decimal places)
Therefore, the dog needs approximately 83.985 Joules of kinetic energy to jump a distance of 1.2 m.