Question

Use the work energy theorem to solve each of these problems and neglect air resistance in all cases. a) A branch falls from the top of a 98.0 m tall redwood tree, starting from rest. How fast is it moving when it reaches the ground? b) A volcano ejects a boulder directly upward 545 m into the air. How fast was the boulder moving just as it left the volcano?

Answer 1

Answer:

a)43.8 m/s

b)103.54 m/s

Explanation:

Work energy theorem

Δ$E_{k}=$ Δ$E_{g}$

$E_{k2} - E_{k1}=-(E_{g2} - E_{g1})\\\\ \frac{1}{2} mv^{2}_{2}- \frac{1}{2} mv^{2}_{1}+ mgh_{2} - mgh_{1} = 0$

a) In this part v1=0 and h2=0

$\frac{1}{2} mv^{2}_{2}- \frac{1}{2} mv^{2}_{1}+ mgh_{2}- mgh_{1} = 0\\\\\\\\\v_{2} =\sqrt{2gh_{1}} = \sqrt{2*9.8*98} =43.8 m/s$=0

b) in this part v2=0, h1= 0, and h2= 545m

$\frac{1}{2} v^{2}_{1}= gh_{2} \\v_{1} =\sqrt{2gh_{2}}=103.54m/s$