Question

Suppose you roll a disk up a slope with an initial velocity v=17m/s at a 33 degree angle. When will it come to rest?

Answer 1

Question #37224

Suppose you roll a disk up a slope with an initial velocity $v = 17 \, \text{m/s}$ at a 33 degree angle. When will it come to rest?

Answer

According to the equations of moving with the constant acceleration

$$v = v _ {0} - a t \text{ such as the final velocity is equal to zero } v _ {0} = a t, t = \frac {v _ {0}}{a}$$

Where $a$ is the acceleration

According to the second Newton's law

$$\boldsymbol {a} = \frac {F}{m} \text{ where } F \text{ is the vertical component of gravitational force (weight) } m \text{ is the mass}$$ $$F = m g \sin \alpha \text{ where } \alpha \text{ is the angle of the slope}$$ $$\boldsymbol {a} = \boldsymbol {g} \sin \alpha$$ $$t = \frac {v _ {0}}{g \sin \alpha}$$ $$S = \frac {17}{9.8 \sin 33{}^{\circ}} = 3.2 \text{ sec}$$

Answer: after 3.2 sec.