Calculating the Impact of a Hammer on a Lawn

[loka]

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...??

 

[rl.bhat]

It appears to be correct.

 

[nlightner]

I would suggest double-checking your calculations and equations to ensure accuracy. It is important to use consistent units throughout your calculations, and to also consider the effects of air resistance and the shape of the hammer on its trajectory. Additionally, it may be helpful to draw a diagram of the situation to visualize the problem and make sure all variables are accounted for. Finally, it would be beneficial to compare your results to real-world observations or data to validate your calculations.