You throw a 5.5 g coin straight down at 4.0 m/s from a 35-m-high bridge. (b) What is the speed of the coin just as it hits the water?

Verified step by step guidance

1. Identify the initial conditions of the problem: initial velocity (v_i) is -4.0 m/s (negative because it is thrown downward), initial position (y_i) is 35 m, and the acceleration due to gravity (a) is approximately -9.8 m/s^2 (negative as it acts downward).
2. Use the kinematic equation that relates initial velocity, acceleration, displacement, and final velocity: v_f^2 = v_i^2 + 2a(y_f - y_i). Here, v_f is the final velocity, and y_f is the final position (which is 0 m at the water surface).
3. Substitute the known values into the equation: v_f^2 = (-4.0 m/s)^2 + 2(-9.8 m/s^2)(0 m - 35 m).
4. Simplify and solve the equation for v_f (final velocity). Remember to take the square root of both sides to solve for v_f, and consider the negative root because the coin is moving downward.
5. The final velocity v_f obtained from the equation will be the speed of the coin just as it hits the water, but remember to convert it to a positive value since speed is a scalar quantity.

Key Concepts

Kinematics

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this problem, kinematic equations can be used to relate the initial velocity, final velocity, acceleration due to gravity, and the distance fallen to determine the speed of the coin just before it hits the water.

Acceleration due to Gravity

Acceleration due to gravity is the acceleration experienced by an object when it is in free fall near the Earth's surface, typically denoted as 'g' and approximately equal to 9.81 m/s². This constant acceleration affects the motion of the coin as it falls, increasing its velocity over time. Understanding this concept is crucial for calculating the final speed of the coin as it descends from the bridge.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the potential energy of the coin at the height of the bridge is converted into kinetic energy as it falls. By applying this principle, one can calculate the final speed of the coin by equating the initial potential energy to the kinetic energy just before impact.