Final answer:
The dog's body rises approximately 5.2 meters above the earth when it jumps to catch the frisbee, which is calculated using the kinematic equation with the initial velocity and acceleration due to gravity.
Step-by-step explanation:
To find out how high a dog jumps straight up to catch a frisbee at a velocity of 10.1 m/s, we use the kinematic equations of motion under gravity, assuming no air resistance and that the jump takes place on Earth. The key concept here is the conservation of energy or the use of kinematic equations to relate the initial velocity to the maximum height when the final velocity at the top of the jump is zero.
We can use the equation for the conservation of kinetic and potential energy or the kinematic equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (which is -9.8 m/s² on Earth, where the negative sign indicates that it's in the opposite direction of the initial velocity), and s is the displacement (the height in this case).
When the dog reaches the maximum height, its velocity is 0 m/s. Rearranging the equation to solve for s, we get:
s = (v² - u²) / (2a)
Plugging in the given values:
s = (0 - (10.1 m/s)²) / (2 * -9.8 m/s²)
s = (0 - 102.01 m²/s²) / (-19.6 m/s²)
s = 102.01 m²/s² / 19.6 m/s²
s ≈ 5.2 m
Therefore, the dog's body rises approximately 5.2 meters above the earth when it jumps to catch the frisbee.