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

a)43.8 m/s

b)103.54 m/s

Step-by-step explanation:

Work energy theorem

Δ
`E_(k)=` Δ
`E_(g)`

`E_(k2) - E_(k1)=-(E_(g2) - E_(g1))\\\\ (1)/(2) mv^(2)_(2)- (1)/(2) mv^(2)_(1)+ mgh_(2) - mgh_(1) = 0`

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

`(1)/(2) mv^(2)_(2)- (1)/(2) mv^(2)_(1)+ mgh_(2)- mgh_(1) = 0\\\\\\\\\v_(2) =\sqrt{2gh_(1)} = √(2*9.8*98) =43.8 m/s`=0

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

`(1)/(2) v^(2)_(1)= gh_(2) \\v_(1) =\sqrt{2gh_(2)}=103.54m/s`