Chapter 2, Problem 61GP

(a)

To determine

To show: Speed of the car before reaching the groundis $v=\sqrt{2gH}$

Explanation of Solution

Given:

Car is moving vertically downwards

Formula used:

Kinetic energy = $\frac{1}{2}m{v}^2$

Potential energy = mgH

Calculation:

Consider Car is moving vertically downwards having mass m , g is acceleration due to gravity, h is the height from which the car is falling down.

Hence the kinetic energy is to be equal to the potential energy,

  $\begin{array}{l}\frac{1}{2}m{v}^2=mgH\\ \frac{1}{2}{v}^2=gH\\ v=\sqrt{2gH}\end{array}$

Conclusion:

Therefore, speed of the car just before hitting the ground is $v=\sqrt{2gH}$

(b)

To determine

Height corresponding to a collision at a given speed.

Answer to Problem 61GP

Height associate to the speed 60 Km/hr. is 14.16 meters

Explanation of Solution

Given:

Speed of the car just before hitting the ground is 60 km/hr

Formula used:

The relation between velocity and height is

  $v=\sqrt{2gH}$

Calculation:

Convert the speed.

60 km/hr= $60\times \frac{1000}{60\times 60}=16.66\text{ m/s}$

Substituting the values,

  $\begin{array}{l}v=\sqrt{2gH}\\ {\left(16.66\right)}^2=2\times 9.8\times H\\ 277.56=19.6\times H\\ H=14.16\text{m}\end{array}$

Conclusion:

Height associate to the speed 60 km/hr is 14.16 meters

(c)

To determine

Height associated at the given speed.

Answer to Problem 61GP

Height associated to the speed 100 km/hr. is 39.3 meters

Explanation of Solution

Given:

Speed of the car just before hitting the ground is 100 km/hr

Formula used:

The relation between velocity and height is

  $v=\sqrt{2gH}$

Calculation:

Convert the speed.

100 km/hr= $100\times \frac{1000}{60\times 60}=27.78\text{m/s}$

Substituting the values.

  $\begin{array}{l}v=\sqrt{2gH}\\ {\left(27.78\right)}^2=2\times 9.8\times H\\ 771.7284=19.6\times H\\ H=39.3\text{m}\end{array}$

Conclusion:

Therefore, height associated to the speed 100 km/hr is 39.3 meters