Question

question 2
5 points
you give a mass of 0.5 kg an initial velocity of 3 m/s up a frictionless incline. to what height will the mass rise (in meters)?
a 4.5
b 2.25
c 0.92
d 0.46

Explanation:

Step1: Apply conservation of mechanical energy

$$E_{initial}=E_{final}$$
The initial energy is kinetic energy \(E_{k}=\frac{1}{2}mv^{2}\), and the final energy is gravitational potential energy \(E_{p} = mgh\). So \(\frac{1}{2}mv^{2}=mgh\).

Step2: Solve for \(h\)

Cancel out \(m\) from both sides of the equation \(\frac{1}{2}v^{2}=gh\). Then \(h=\frac{v^{2}}{2g}\). Given \(v = 3\space m/s\) and \(g=9.8\space m/s^{2}\), substitute the values: \(h=\frac{3^{2}}{2\times9.8}=\frac{9}{19.6}\approx0.46\space m\)

Answer:

D. 0.46