Chapter 11, Problem 69A

To determine

Height from which car have to be dropped.

Answer to Problem 69A

39.37 m

Explanation of Solution

Given:

Speed of the car, $v=1\times {10}^2=100\text{ km/hr}$

Formula Used:

When car is dropped from any height then its potential will change in kinetic energy.

  $mgh=\frac{1}{2}m{v}^2$

Here, m is the mass, g is the gravitational acceleration and v is the speed.

Calculations:

Speed of the car is given $v=100\text{ km/hr}$

  $1\text{ km = 1000 m, 1 hour =3600 s}$

Therefore speed in m/sec will be:

  $\begin{array}{c}100\text{ km/hr =100}\times \frac{1000\text{ m}}{3600\text{ s}}\\ =27.78\text{ m/s}\end{array}$

  $\begin{array}{l}mgh=\frac{1}{2}m{v}^2\\ gh=\frac{1}{2}{v}^2\\ v^2=2gh\\ {27.78}^2=2\times 9.8\times h\\ 19.6h=771.73\\ h=\frac{771.73}{19.6}\\ =39.37\text{ m}\end{array}$

Conclusion:

Therefore, car is dropped from a height of 39.37 m.