Impulse, Momentum, and Collision: Exploring Physics Concepts with Optimism

1) When you jump off a diving board into water, the water deforms upon impact, extending the time of impact for your body's momentum to reach zero. This longer duration lessens the force felt due to the impact, resulting in a safe and uninjured landing. On the other hand, jumping onto concrete offers no deformation, leading to a very short time for your momentum to reach zero, causing a significant force that can be harmful. This phenomenon is explained by the principles of impulse and momentum.

Explanation:

Jumping into Water: When you jump into water, the water absorbs some of the impact energy by deforming. This deformation extends the time it takes for your body's momentum to reach zero, reducing the force exerted on your body. According to Newton's second law of motion, the rate of change of momentum is proportional to the force produced. Therefore, the longer time of impact in water reduces the force experienced during the landing.

Jumping onto Concrete: In contrast, concrete does not deform upon impact, providing a very short duration for your momentum to reach zero. As a result, the force exerted on your body upon landing is significantly higher, making it a harmful and dangerous landing. Your body may attempt to deform in a bid to reduce the force, but the impact can still be lethal due to the rigid nature of the surface.

2) The linebacker and quarterback, with their respective masses and velocities, collide in midair with the linebacker holding onto the quarterback. After the collision, they move off together. What is their combined velocity in terms of magnitude and direction?

Explanation:

Given Data:
Mass of Linebacker (M1) = 125 kg
Mass of Quarterback (M2) = 80 kg
Velocity of Linebacker (V1) = 2.5 m/s (to the right)
Velocity of Quarterback (V2) = 3 m/s (to the left)

Using the principle of momentum conservation, the total initial momentum must be equal to the total momentum after the collision. The equation for this scenario is:
M1V1 + M2V2 = (M1 + M2) Vf

Where Vf represents the final velocity of the linebacker and quarterback moving together. Since the collision is inelastic, the masses stick together after the collision.

Solving for the final velocity:
(125 x 2.5) + (80 x 3) = (125 + 80) Vf
312.5 + 240 = 205 Vf
552.5 = 205 Vf
Vf = 552.5 / 205 = 2.69 m/s

Therefore, after the collision, the linebacker and quarterback move together with a velocity of 2.69 m/s towards the right. This velocity is a result of the momentum conservation principles and the combined masses and velocities of the individuals involved in the collision.