17. A small dog is trained to jump straight up a distance of 1.1 m. How much kinetic energy does the 7.7-kg dog need to jump this high? (The acceleration due to gravity is 9.8 m/s2.) Show your work. (3 points)
85J
To calculate the kinetic energy required for the dog to jump, we need to determine the change in potential energy. The potential energy is given by the formula P.E. = mgh, where m is the mass of the dog, g is the acceleration due to gravity, and h is the height.
Given:
Mass of the dog (m) = 7.7 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Height (h) = 1.1 m
First, let's calculate the potential energy at the highest point of the jump:
P.E. = mgh
P.E. = 7.7 kg * 9.8 m/s^2 * 1.1 m
P.E. = 84.482 J (Joules)
The potential energy at the highest point is 84.482 Joules.
Since the dog starts from the ground, the initial potential energy is zero. Therefore, the kinetic energy required to jump this high is equal to the change in potential energy.
Kinetic Energy (K.E.) = Change in Potential Energy
K.E. = 84.482 J
Hence, the dog needs approximately 84.482 Joules of kinetic energy to jump a height of 1.1 meters.