A bungee jumper (m = 66.00 kg) tied to a 39.00 m cord, leaps off a 69.00 m tall bridge. He falls to 5.00 m above the water before the bungee cord pulls him back up. What size impulse is exerted on the bungee jumper while the cord stretches?

To find the impulse exerted on the bungee jumper while the cord stretches, we need to calculate the change in momentum experienced by the jumper.

Impulse (J) is defined as the change in momentum (Δp) and can be calculated using the formula:

J = Δp

Momentum (p) is defined as the product of an object's mass (m) and its velocity (v) and can be calculated using the formula:

p = m * v

Since the bungee jumper is falling vertically down, the initial momentum (p1) when he jumps off the bridge is zero because his initial velocity is zero. Hence, the impulse will be equal to the final momentum (p2) when the bungee cord pulls him back up.

To find the final momentum, we need to calculate the velocity of the bungee jumper just before the cord starts pulling him back up. We can use the principle of conservation of mechanical energy to find this.

At the highest point of the jumper's fall (5.00 m above the water), all of the gravitational potential energy (PE) has been converted into kinetic energy (KE).

PE = m * g * h (potential energy)
KE = (1/2) * m * v^2 (kinetic energy)

Setting these equal, we can find the velocity (v).

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

Simplifying the equation:

v^2 = 2 * g * h

v = √(2 * g * h)

where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height (5.00 m).

Substituting the values, we can calculate v:

v = √(2 * 9.8 * 5)

Now that we have the velocity just before the cord pulls the jumper back up, we can calculate the final momentum (p2):

p2 = m * v

Lastly, the impulse exerted on the bungee jumper while the cord stretches is equal to the change in momentum:

J = p2 - p1

Since p1 is zero, J = p2.

Now, you can substitute the given values (mass, height, etc.) into these equations to calculate the impulse exerted on the bungee jumper while the cord stretches.