Q. 27 A car traveling at 30 m/s runs o... [FREE SOLUTION]

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Chapter 2: Q. 27 (page 60)

A car traveling at 30 m/s runs out of gas while traveling up a 10掳 slope. How far up the hill will it coast before starting to roll back down?

Short Answer

Expert verified

The distance travelled by car before it rolls back is 260.2 m.

Step by step solution

Step 1. Write the given information

The car is traveling at the initial speed $u = 30 m / s$

The car is traveling on the slope inclined at the angle 10^o.
If the gas runs out, then the car would stop and starts rolling back. Before, it starts rolling the velocity of the car would be $v_{f} = 0 m / s e c$

Acceleration due to gravity is $g = 10 m / s e c$

The deceleration of the car is given by

localid="1648196205233" $a = g \sin 螛 a = 10 (\sin 10 掳) a = 1.73 m / s^{2}$

Step 2. To determine the distance traveled by car before it rolls back

Let the time taken by the car until it starts rolling is $t$ .
Write the equation and substitute the known variables
$v = u + a t 0 = 30 + (- 1.73) t t = \frac{30}{1.73} = 17.34 s e c$

Thus, the time taken by a car to stop and roll back is 17.34 sec
Now, let the distance covered by the car is $S$
Using the equation of motion,
localid="1648466936650" $S = u t + \frac{1}{2} a t^{2} S = 30 (17.3) + \frac{1}{2} (- 1.73) {(17.3)}^{2} S = 519 - 258.8 S = 260.2 m$

Hence, the distance traveled by car before it rolls back is 260.2 m.