Answered: Physics Question

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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Step 1

Given, four cases.

We know that free-fall motion is independent of mass.

Finding the amount of time t it takes to hit the ground.

(1) Using the kinematic equation to find t. Downward direction is taken as the negative y-axis:

Symbols used have their usual meanings.

$y - y_{0} = v_{0 y} t - \frac{1}{2} g t^{2}$

Substituting the known values, the initial velocity is zero.

$\begin{array}{rcl} - 10 - 0 & = & (0) t - \frac{1}{2} (9.81) t^{2} \\ t^{2} & = & \frac{2 \times 10}{9.81} \\ t & = & \sqrt{\frac{2 \times 10}{9.81}} \\ t & = & 1.43 s \end{array}$

(2) Since, there is no x-component of initial velocity, we will take $v_{0 y} = 10 \frac{m}{s}$

$y - y_{0} = v_{0 y} t - \frac{1}{2} g t^{2}$

Substituting the known values:

$- 10 - 0 = (10) t - \frac{1}{2} (9.81) t^{2} 4.9 t^{2} - 10 t - 10 = 0 Solving this quadratic equation, we get : t = \frac{- (- 10) \pm \sqrt{{(10)}^{2} - 4 (4.9) (- 10)}}{2 (4.9)} t = \frac{10 \pm 17.2}{9.8} Taking the positive value of time as negative time do not make any sense : t = \frac{10 + 17.2}{9.8} t = \frac{27.2}{9.8} t = 2.77 s$

(3) Since, there is no x-component of initial velocity, we will take $v_{0 y} = 10 \frac{m}{s}$

The answer will be the same as part (2)

$t = 2.77 s$

(4) Since, there is no x-component of initial velocity, we will take $v_{0 y} = 10 \frac{m}{s}$

$- 15 - 0 = (10) t - \frac{1}{2} (9.81) t^{2} 4.9 t^{2} - 10 t - 15 = 0 Solving this quadratic equation, we get : t = \frac{- (- 10) \pm \sqrt{{(10)}^{2} - 4 (4.9) (- 15)}}{2 (4.9)} t = \frac{10 \pm 19.8}{9.8} Taking the positive value of time as negative time do not make any sense : t = \frac{10 + 19.8}{9.8} t = \frac{29.8}{9.8} t = 3.04 s$