A bolt is dropped from a bridec undering 90 m construction, fall- to the valley below the bridg

A bolt is dropped from a bridec undering 90 m construction,...

A bolt is dropped from a bridec undering $90 \mathrm{~m}$ construction, fall- 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 (c) when it reaches the valley bencath the bridge?

Key Concepts

Quadratic Equations in Kinematics

In many kinematics problems, particularly those involving displacement calculations over a specific interval, the equations reduce to quadratic forms. Solving these quadratic equations is necessary to determine the time intervals or initial conditions required for the analysis of motion.

Kinematic Equations for Constant Acceleration

These equations, such as s = ut + ½at² and v = u + at, are instrumental in solving problems involving uniformly accelerated motion. They provide a method to calculate displacement, velocity, and time when an object is moving under constant acceleration, which is critical in analyzing free-fall scenarios.

Free-Fall Motion

Free-fall motion describes the behavior of objects falling solely under the influence of gravity, with a constant acceleration of approximately 9.8 m/s² (ignoring air resistance). This concept is fundamental for determining the time, displacement, and velocity of objects in vertical motion.

Kinematics

This is the branch of mechanics that deals with the motion of objects, without considering the forces that cause the motion. It uses mathematical equations to relate displacement, velocity, acceleration, and time, which are essential for analyzing motion such as free-fall.

Transcript

00:01 In this problem of motion along a straight line we have given that this is a bolt is dropped from a bridge under construction falling 90 meters to the valley below the bridge.

00:17 Now we have to find this is we can say delta h is equals to 90 meters.

00:25 Now we have to find in how much time does it pass through the 20 % of its fall.

00:32 And also we have to find what is its speed when it begins that last 20 % of its fall.

00:41 So first for first part we have to find the time.

00:46 Since this is in the free fall, so equation we have to follow is say i'm writing it.

00:53 Say delta h would be here y minus y not and this value would be the function say y minus y not is equals to minus half g and so, this is the formula and if we choose upward the positive y direction, then the time for the full fall would be say this is equal to 90 and minus 1 divided with 2 and g is equal to 9 .8 meters per second square and when we solve for t so t is equal to 4 .29 second.

01:33 That means total time for falling 90 meters is equal to 4 .2 seconds.

01:34 That means total time for falling 90 meters is equal to 4 .2.

01:37 2 .9 seconds.

01:40 And now we have asked that in how much time does it pass through last 20 % of its fall.

01:48 So first we have to calculate 80 % of falls.

01:51 So we can say 80 % of fall which is equal to of 90 meters.

01:56 This value would be 72 meters...