Physics Practice Problems Vertical Motion & Free Fall Practice Problems Solution: A hoodlum throws a stone vertically downward with ...

Solution: A hoodlum throws a stone vertically downward with an initial speed of 12.0m/s from the roof of a building, 30.0m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the stone at impact?

Problem

A hoodlum throws a stone vertically downward with an initial speed of 12.0m/s from the roof of a building, 30.0m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the stone at impact?

Solution

We're asked for the time of flight and final velocity of the vertically-thrown stone.

Whenever we have a problem where an object is dropped or thrown from some height, it is affected only by the constant acceleration of gravity (g = 9.8 m/s) after being released, and therefore we can use the kinematics (UAM) equations. Because the motion is in the vertical direction, we'll replace Δx with Δy. Our standard coordinate system has the +y-axis pointing upwards, so we say = −g = −9.8 m/s2. To solve, we'll follow these steps:

  1. Identify the target variable for each part of the problem.
  2. Identify which variables are known—remember that only 3 of the 5 variablesy, v0, vf, a, and t) are needed to solve any kinematics problem, and we already know what a is.
  3. Choose a UAM equation with only one unknown, which should be our target variable.
  4. Solve the equation for the target variable, then substitute known values and calculate the answer.

 vf = v0 -gty= (vf+v02)ty= v0t-12gt2 vf2= v02 -2gy

Remember that down is the −y-direction, and make sure you're using the right sign for any velocities and displacements in the problem!

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