Answer to Question #94879 in Mechanics | Relativity for Alexis

Question

Celia Mae starts a ball rolling up a 4.5° hill on a planet where g is half of that on Earth with a velocity of 3.2 m/s. Once she starts it moving, she just watches it roll.

A. How far does the ball roll up the incline before it stops?
B. How long does it take the ball to stop?
C. How far does the ball roll up the incline in 2.5 seconds?

Answer 1

A. From the conservation of energy:

$$0.5mv^2=m(0.5g)s\sin{4.5\degree}$$

$$3.2^2=9.8\sin{4.5\degree}s$$

$$s=13.3\ m$$

B.

$$t=\frac{v}{0.5g\sin{4.5\degree}}=\frac{2(3.2)}{9.8\sin{4.5\degree}}=8.3\ s$$

C.

$$d=vT-0.5(0.5g)\sin{4.5\degree}T^2$$

$$d=(3.2)(2.5)-0.25(9.8)\sin{4.5\degree}2.5^2=5.6\ m$$