A ball is dropped from rest from the top of a 40.0 m building. A second ball is thrown downward

step 1 In this question it is given that a ball is dropped from rest from the top of a 40 meter buildin

A ball is dropped from rest from the top of a 40.0 m...

A ball is dropped from rest from the top of a $40.0 \mathrm{m}$ building. A second ball is thrown downward 1.0 s later. (a) If they hit the ground at the same time, find the speed with which the second ball was thrown. (b) What is the ratio of the speed of the thrown ball to the speed of the other as they hit the ground? (Take the acceleration due to gravity to be $10.0 \mathrm{m} \mathrm{s}^{-2} .$

A ball is dropped from rest from the top of a $40.0 \mathrm{m}$ building. A second ball is thrown downward 1.0 s later.
(a) If they hit the ground at the same time, find the speed with which the second ball was thrown.
(b) What is the ratio of the speed of the thrown ball to the speed of the other as they hit the ground? (Take the acceleration due to gravity to be $10.0 \mathrm{m} \mathrm{s}^{-2} .$

Key Concepts

Kinematic Equations

These are the fundamental equations used to describe motion under constant acceleration. They relate displacement, initial velocity, time, acceleration, and final velocity. For example, the equation s = ut + ½at² is key when analyzing objects released or thrown in gravitational fields. This allows the calculation of distances travelled and velocities reached over a given time interval.

Uniform Gravitational Acceleration

This concept refers to the constant acceleration experienced by any object in free fall near the Earth’s surface, typically approximated as 9.8 m/s² or 10.0 m/s². It is crucial for solving problems related to free-falling objects since it simplifies the motion analysis by providing a constant value for acceleration.

Time Delay in Motion Initiation

When two objects are set in motion at different times, analyzing their motion involves accounting for the delay in start times. This concept is essential when synchronizing events, such as ensuring two objects meet at the same point at the same time despite starting at different moments. It requires calculating separate time intervals for each object based on their individual start times and motions.

Speed Ratio Analysis

After finding the velocities of two objects acting under gravity, comparing their speeds through ratios can provide insights into their relative motion. This analysis is important in problems where understanding the proportion between different speeds at impact or other events helps in grasping the dynamics of motion and the effects of initial conditions on final outcomes.

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