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5. Derive a formula for the amount of time it takes for something to hit the ground if it is dropped from a height h. You should get an equation solved for t in terms of h and g.

5. Derive a formula for the amount of time it takes for something to hit the ground if it is dropped from a height h. You should get an equation solved for t in terms of h and g.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem 5:** Derive a formula for the amount of time it takes for an object to hit the ground if it is dropped from a height \( h \). You should get an equation solved for \( t \) in terms of \( h \) and \( g \). **Additional Content:** To solve this problem, we start by using the equation of motion for free fall, which assumes no air resistance: \[ h = \frac{1}{2} g t^2 \] Where: - \( h \) is the height from which the object is dropped, - \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \) on the surface of the Earth), - \( t \) is the time in seconds it takes for the object to reach the ground. To find the time \( t \), we rearrange the formula: \[ t^2 = \frac{2h}{g} \] \[ t = \sqrt{\frac{2h}{g}} \] This equation gives us the time \( t \) it takes for an object to fall to the ground from height \( h \) under the influence of gravity \( g \).
Transcribed Image Text:**Problem 5:** Derive a formula for the amount of time it takes for an object to hit the ground if it is dropped from a height \( h \). You should get an equation solved for \( t \) in terms of \( h \) and \( g \). **Additional Content:** To solve this problem, we start by using the equation of motion for free fall, which assumes no air resistance: \[ h = \frac{1}{2} g t^2 \] Where: - \( h \) is the height from which the object is dropped, - \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \) on the surface of the Earth), - \( t \) is the time in seconds it takes for the object to reach the ground. To find the time \( t \), we rearrange the formula: \[ t^2 = \frac{2h}{g} \] \[ t = \sqrt{\frac{2h}{g}} \] This equation gives us the time \( t \) it takes for an object to fall to the ground from height \( h \) under the influence of gravity \( g \).
**Problem 4: Kinematics of a Tossed Pen** Bob tosses a pen straight up into the air, but does not catch it, so it falls to the floor. The speed of the pen is 3.7 m/s when it leaves his hands, and his hands are 1.2 m above the floor. - **a)** What is the sign of the pen’s velocity: - On the way up? - At the top? - On the way down? What about the sign of its acceleration: - On the way up? - At the top? - On the way down? - **b)** How long was the pen in the air? - **c)** What is the pen’s velocity just before it hits the floor? - **d)** What is the maximum height above the floor that the pen reaches? - **e)** What is the pen’s velocity just as it passes by Bob’s hands on the way down?
Transcribed Image Text:**Problem 4: Kinematics of a Tossed Pen** Bob tosses a pen straight up into the air, but does not catch it, so it falls to the floor. The speed of the pen is 3.7 m/s when it leaves his hands, and his hands are 1.2 m above the floor. - **a)** What is the sign of the pen’s velocity: - On the way up? - At the top? - On the way down? What about the sign of its acceleration: - On the way up? - At the top? - On the way down? - **b)** How long was the pen in the air? - **c)** What is the pen’s velocity just before it hits the floor? - **d)** What is the maximum height above the floor that the pen reaches? - **e)** What is the pen’s velocity just as it passes by Bob’s hands on the way down?
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