Forces in 2 dimensions help please!!?

Question

A hammer slides down a roof that makes a 32degree angle with the horizontal. What are the magnitudes of the components of the hammer's velocity at the edge of the roof if it is moving at a speed of 6.25 m/s

please help me understand how to do this problem please! i will choose a best answer

Answer 1

Given:
vi = 6.25m/s
angle = 32 degrees

Find:
vfx = ?
vfy = ?

Solution:

FIRST,
vix = vi (cos theta)
vix = 6.25 m/s (cos 32 degrees)
vix = 5.300300601 m/s

SECOND,
viy = vi (sin theta)
viy = 6.25m/s ( sin 32 degrees)
viy = 3.311995401 m/s

THIRD,
t = vi (sin theta)/g
t = (6.25m/s) (sin 32 degrees)/(9.8m/s^2)
t = 6.25m/s (0.529919264)/(9.8m/s^2)
t = 0.337958714 s

FOURTH
vfy = viy +gt
vfy = 6.25m/s + (9.8m/s^2)(0.337958714 s)
vfy = 9.561995397 m/s

FIFTH,
*Velocity of the horizontal component is always constant!



Thus, the magintude of the final velocities..
a)horizontal component = 5.300300601 m/s
or 5.3 m/s
b)vertical component = 9.561995397 m/s or 9.6m/s

Good luck and God bless!

Answer 2

Here, velocity can be broken down into two components: (1) Vertical or (2) Horizontal.

We know the roof's angle. So we know the direction of the hammer as it slides down. The vertical (up/down) component is Vy=v*sin(theta) and the horizontal component is Vx=v*cos (theta).

(These components also go back to your pythagorean thereom)

Now to solve

Vy= 6.25 sin (-32) and
Vx= 6.25 cos (-32)

Note the -32 degrees is because the direction of travel is downward
therefore

Vy= -3.31 m/sec
Vx= 5.30 m/sec

Good luck

Answer 3

vectors need a coordinate axis. let the horizontal be the x axis and vertical be y axis with up being pos y and right being pos x.
go here to look at this coordinate axis and draw one on your paper. http://www.purplemath.com/modules/plane3.htm
a vector cannot have meaning without an origin and a coordinate axis. draw a line in quadrant IV. the line goes from the origin and it makes a 32 degree angle with the positive x axis. drop a perpendicular line from the x axis down to the tip of the first line. now you have a right triangle and trigonometry or pythagarean theorm will let you find all the numbers.