How Do You Calculate Displacement and Time of Flight When Sliding Off a Roof?

[Inertialforce]

Homework Statement

On a snowy winter day, you decide to slide off the roof of your home. The roof has an angle of inclination equal to 25.0 degrees. Given that you leave the edge of the roof with a velocity of 5.36m/s and the edge of the roof is 9.25m above the ground level. Determine:

a)Your total horizontal displacement
b)Your total time of flight

Homework Equations

Vx = dx/t
Vfy = Viy -gt
Vfy(squared) = Viy(squared) - 2gdy

The Attempt at a Solution

First I wrote down what I was given and what I could easily derive:

theta = 25(degrees)
h = dy = 9.25m
Viy = 5.36m/s
g = 9.80m/s

Vx = (cos(25))(5.36) = 4.8578 m/s

Then I went:
Vfy(squared) = Viy(squared) - 2gdy

I then put in my values and the answer I got for Vfy is:

Vfy = 14.5m/s

Then I used the equation:

Vfy = Viy -gt

and I isolated the t and plugged in all my variables and the answer I got for t is:

t = 0.933s

Then I used the equation:

Vx = dx/t
(Vx)(t) = dx

I then plugged in the two values (Vx and t) which I found out from my previous calculations and I got an answer for dx:

dx = 4.53m

b) For part "b" I used the equation:

Vfy = Viy - 2gt

then I isolated the t value and put in my values (some of which I found out in part a) to solve for t and I got:

t= 0.933s

I know this may seem like a really long question but could someone double check the answers that I got or tell me if the method I used in both question is correct or not? I would greatly appreciate it.

 

[rl.bhat]

you leave the edge of the roof with a velocity of 5.36m/s in the direction of the inclination of the roof. There fore Viy = sin(25)(5.36)

 

[thomate1]

Your method and answers seem to be correct. However, I would suggest using the equation d = v0t + (1/2)at^2 to calculate the horizontal displacement in part a), as it takes into account both the initial velocity and the acceleration due to gravity. Also, in part b), you can use the same equation with the vertical displacement (in this case, the height of the roof) and the initial vertical velocity to solve for the time of flight. Keep up the good work!