Question

A common trick for a show dog is to jump vertically upward off its hind legs. A particular dog of mass =10.5 kg shows off its jumping ability by jumping straight up and rising d = 0.548 m off the ground. What impulse did this dog receive from the ground in order to pull this off?

Answer 1

To calculate the impulse received by the dog, the final velocity of the dog just before leaving the ground must be determined using the conservation of energy principle, after which the impulse can be calculated as the product of the dog's mass and this final velocity.

Step-by-step explanation:

To calculate the impulse received by the dog, we can use the relationship between impulse (I) and the change in momentum (\(\Delta p\)) of the dog due to its jump. Impulse is defined as the product of the force (F) and the time over which it acts (\(\Delta t\)), and it is also equal to the change in momentum:

Impulse (I) = F * \(\Delta t\) = \(\Delta p\) = m * v

First, we need to determine the final velocity (v) the dog had just before leaving the ground using the conservation of energy principle for the vertical jump:

Potential energy at the highest point = Kinetic energy just before leaving the ground

m * g * d = (1/2) * m * v^2

Solving for v, we get:

v = \(\√{2 * g * d}\)

Now we can find the impulse by calculating the change in momentum:

\(\Delta p\) = m * v

\(\Delta p\) = 10.5 kg * \(\√{2 * 9.81 m/s^2 * 0.548 m}\)

The calculated change in momentum is the impulse the dog received from the ground in order to make the jump.

Answer 2

The impulse received by the dog is calculated using the final velocity determined from the distance it jumps vertically and its mass, applying the kinematic equation and impulse-momentum theorem.

Step-by-step explanation:

The student is asking about the impulse received by a dog when it jumps vertically upward.

First, we must determine the dog's final velocity just before it leaves the ground using the kinematic equation for motion under constant acceleration (gravity in this case):

vf² = vi² + 2ad

Where vf is the final velocity, vi is the initial velocity (which is 0 in this case), a is the acceleration (9.8 m/s²for gravity), and d is the distance (0.548 m).

Upon solving for vf, we use the impulse-momentum theorem, which states:

Impulse = Change in Momentum = mvf - mvi

Since the dog starts from rest (vi = 0), the impulse is simply:

Impulse = mvf

We can calculate the final velocity vf and then multiply it by the mass of the dog (10.5 kg) to find the impulse.