Question

Given is the direction of velocity of the object on an incline of ${45}^o$.

Let R be the range of the projectile in meters along the inclined plane.(Take $g=9.8m/s^2$).Find R/10 rounded to the nearest integer.

Answer 1

Assume $x$ is the direction along the plane and $y$ is the direction perpendicular to the plane

For $y$ direction:
$h=0=\left(20\sqrt{2}\sin {15}^{\circ }t\right)-\left(\frac{1}{2}\right)9.8\cos {30}^o{t}^2$
$t=\frac{40\times 1.414\sin 15}{\left(9.8cos30\right)}=1.72$ sec

Along $x$ direction
$x=20\sqrt{2}\cos {15}^{\circ }\times 1.72-\frac{1}{2}g\sin {30}^o(1.72{)}^2=39$ m