Impulse And Momentum

We will use the impulse-momentum theorem to relate the force applied to the golf ball to the change in its momentum.

Step 1: Define the variables

• Mass of the golf ball, gm = kg
• Final velocity of the golf ball, m/s
• Initial velocity of the golf ball, m/s
• Time of contact, s
• Force at the beginning of the contact = (what we need to find)

Step 2: Impulse-Momentum Theorem

The impulse, , is equal to the change in momentum: Also, the impulse is the integral of force over time:

Step 3: Force as a Function of Time

Since the force decreases linearly with time, we can express it as: where is the initial force (at ) and is the time of contact, which is s in this case.

Step 4: Calculate the Impulse

Now, we calculate the impulse by integrating the force function over time:

Step 5: Apply the Impulse-Momentum Theorem and Solve for

Now, equating the impulse to the change in momentum:

Plugging in the given values:

Therefore, the force at the beginning of the contact is N.