Calculating the Impact of a Hammer on a Lawn

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SUMMARY

The discussion centers on calculating the impact distance of a hammer that slides down a roof inclined at 60 degrees and falls 11 meters to the lawn. Using the equations of motion and forces, the net force acting on the hammer was determined to be 7.36 N, resulting in an acceleration of 7.36 m/s². The time of flight was calculated to be approximately 0.604 seconds, leading to an impact distance of 5.3 meters from the wall. The calculations were confirmed as accurate by participants in the discussion.

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Homework Statement



A hammer slides 21 m down the side of the roof inclined at 60 deg. above the horizontal, and falls down to the lawn 11m below the edge of the roof.

How far away from the wall will this hammer impact with the lawn?

m = 1 kg
mu = 0.23


Homework Equations





The Attempt at a Solution



Fgx = mg sin 60
= (1) (9.8)sin60
= 8.487N

Ff = UFn = 1.127 N

Fnet = Fgx - Ff = 8.487 - 1.127 = 7.36 N

Fnet = ma
a = Fnet/m = 7.36 m/s^2

to find t sub y = 11

y = yo + voyt - 1/2gt^2
0 = 4.9t^2 + 15.23t - 11
t = -15.23 +- (15.23^2 - 4(4.9) (-11)))^sq root

t = -15.23 +- (15.23^2 - 4(4.9) (-11)))^sq root / 2 (4.9)

t = -15.23+- (447.5529)^1/2/ 9.8

then t = 0.06004

sub t = 0.604 into x = Vxt
x = 17.582cos60 (0.604)
x = 5.3 m

5.3 m away from the wall

?? i rly doubt this is rite...??
 
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It appears to be correct.
 

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