Question

A box starts at rest at the top of a $30.0$ degree incline as shown and slides down a diagonal distance of $4.00m$. If the box weighs $2.00kg$ and there is no friction, the speed of the box at the bottom of the incline is most nearly:

• A. $4.43m/s$
• B. $6.26m/s$
• C. $8.24m/s$
• D. $8.86m/s$
• E. Not enough information

Answer 1

The correct option is B $6.26m/s$

Given - $d=4m,\theta ={30}^o$

now the acceleration with which box will go down will be the component of gravitational acceleration , parallel to the surface of incline ,

$a=g\sin 30$

now by $v^2=u^2+2ah$

$v^2=0+2g\sin 30\times 4$

or $v^2=2\times 9.8\times 1/2\times 4=39.2$

or $v=\sqrt{39.2}=6.26m/s$