Momentum question Apply the general results obtained in the full analysis of mot

Question

Momentum question

Apply the general results obtained in the full analysis of motion under the influence of a constant force in Section 2.5 to answer the following questions. You hold a small metal ball of mass m a height h above the floor. You let go, and the ball falls to the floor. Choose the origin of the coordinate system to be on the floor where the ball hits, with y up as usual. Express all results in terms of m, g, and h. Just after release, what are yi and yiy? yi= yiy= Just before hitting the floor, what is yf? How much time delta t does it take for the ball to fall? delta t= What is vfy just before hitting the floor? vfy=

Explanation / Answer

given,

mass = m

height = h

just after release yi = h

just after release viy = 0 m/s

just before hitting the ground the yf = 0

by second euation of motion

s = ut + 0.5 * a * t^2

so u will be 0

h = 0 + 0.5 * g ^ t^2

t = sqrt(2h)/g

by conservation of energy

mgh = 0.5 * m * vfy^2

vfy = sqrt(2gh)

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