Question

Solve this:

​Q24. An automobile moving at a speed of 72 km h^–1 reaches the foot of a smooth incline when the engine is switched off. How much distance does the automobile go up the incline before stopping? The incline makes an angle of 30° with the horizontal. Take g = 9.8 ms^–2.
Ans . 40.8 m.

Answer 1

Dear Student ,
It will move up the plane until the velocity becomes zero.
at the instant when automobile is at the base,
u= 72 Km/s= 20 m/s.
just when it moves up the plane gravity 's sin component cause retardation which is equal to
g sin 30°.
using
$$\begin{gathered} v^2-u^2=2as \\ 0-400=2\times -g\sin {30}^o\times s \\ s=\frac{400}{2\times 9.8\times {\displaystyle \frac{1}{2}}} \end{gathered}$$
then max distance travelled
s = 40.8m

Regards