A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge

step 1 This tells us that a bolt is dropped. So that means the initial velocity is zero. It falls 90 me

A bolt is dropped from a bridge under construction, falling...

A bolt is dropped from a bridge under construction, falling $90 \mathrm{~m}$ to the valley below the bridge. (a) In how much time does it pass through the last $20 \%$ of its fall? What is its speed (b) when it begins that last $20 \%$ of its fall and $(\mathrm{c})$ when it reaches the valley beneath the bridge?

A bolt is dropped from a bridge under construction, falling $90 \mathrm{~m}$ to the valley below the bridge. (a) In how much time does it pass through the last $20 \%$ of its fall? What is its speed
(b) when it begins that last $20 \%$ of its fall and $(\mathrm{c})$ when it reaches the valley beneath the bridge?

Key Concepts

Motion Segmentation

Sometimes, it is useful to divide an object's motion into segments, such as portions defined by specific percentages of the total distance traveled. This approach allows a more detailed analysis of motion during distinct intervals, making it possible to answer questions about the timing and speed at particular stages of the object's fall.

Uniformly Accelerated Motion

This concept refers to motion in which an object experiences a constant acceleration. The basic kinematic equations—like s = ut + ½at² and v = u + at—are used to relate displacement, velocity, time, and acceleration. These equations are crucial for analyzing problems involving free-falling objects and other uniformly accelerated motions.

Free Fall

Free fall describes the motion of an object that is only under the influence of gravity, with air resistance neglected. It is a specific case of uniformly accelerated motion where the acceleration is constant (typically approximated as 9.8 m/s² on Earth). Understanding free fall is essential for solving problems where objects are dropped or thrown under gravity.

Displacement and Velocity Relationships

This involves the use of kinematic formulas to connect how far an object moves (displacement) and how fast it is moving (velocity) over a given time with constant acceleration. These relationships allow one to calculate either the final speed after a given distance or the time taken to cover certain segments of motion.

Quadratic Equations in Kinematics

When applying the kinematic equations to solve for time or displacement, the resulting relationships are often quadratic. Solving these quadratic equations is essential in determining the correct time intervals and velocities, confirming that the mathematical solutions correspond to the physical scenario.