Answer to Question #161024 in Classical Mechanics for Ella

Question

A box (very small) was propelled up an inclined plane. The propelling agent is no longer acting on the box as it moves up the incline. The coefficients of static and kinetic friction for the box/plane interface are 0.4 and 0.2 respectively. The initial speed of the block G the bottom of the incline is 63m/s. The block slides up the plane and becomes a projectile. How high will the box fly and where will it impact the ground?

Answer 1

Given,

The coefficient of static friction $(\mu_s)= 0.4$

coefficient of kinetic friction $(\mu_k) = 0.2$

Initial speed of block $(u)= 63 m/s$

Let the inclination of the plane $=\theta$

and height of the plane $=(h)$

When the block reached to the top of the inclination, then velocity of the block $v^2 = u^2-(g\sin\theta-\mu g\cos\theta)h\sin\theta$

$v=\sqrt{63^2-10h(\sin\theta-0.2\cos\theta)\sin\theta}$

Maximum height reached by the block after the maximum height reached on the plane = $\Rightarrow H=\frac{v\sin\theta}{2g}$

$\Rightarrow H = \frac{\sqrt{63^2-10h(\sin\theta-0.2\cos\theta)\sin\theta}\sin\theta}{2g}$