Projectile motion snowball help

[imAwinner]

[SOLVED] Projectile motion help

A snowball rolls of a barn roof that slopes downward at an angle of 40 degrees. The edge of the roof is 14 m above the ground, and the snowball has a speed of 7 m/s as it rolls off the roof.

a) How far from the edge of the barn does the snowball strike the ground if it doesn't strike anything else while falling?

b) A man 1.9 m tall is standing 4 m from the edge of the barn, will he be hit by the snowball?

My answer is 11.792 m for (a)

x
a=0
v=7cos40=5.36
x=5.36t


y
a=-9.8
v=7sin40-9.8t= 4.5-9.8t
y=4.5t-4.9t^2+14 (is this right?)

When y=0 : 0=-4.9t^2 + 4.5t + 14 (use quadratic equation)
t=2.2
Plug it into x equation: x=5.36(2.2)
x=11.792 m

Now for (b) i don't know what to do. I said x=4 and got t=.746 s
Then I plugged it into the y equation but my answer turned out to be 14.36 which is impossible. Any help is greatly appreciated.

 

[Vijay Bhatnagar]

Your equation for x-axis is correct. However, in the equations along y axis, the initial velocity should be with -ve sign (-4.5 m/s) because it is downward (same reason acceleration g is -ve). As the snowball hits the ground, vertical displacement is -14m (note the -ve sign). Put y=-14 in the second equation and solve for t. Put this value of t in the equation for x to obtain the required distance from the edge of the barn.

To find answer to b) : Determine the time instant when horizontal displacement is 4m. Then determine the vertical displacement (from the top) at that instant. Determine height of the snowball from ground. That will answer b).

 

[imAwinner]

Your equation for x-axis is correct. However, in the equations along y axis, the initial velocity should be with -ve sign (-4.5 m/s) because it is downward (same reason acceleration g is -ve). As the snowball hits the ground, vertical displacement is -14m (note the -ve sign). Put y=-14 in the second equation and solve for t. Put this value of t in the equation for x to obtain the required distance from the edge of the barn.

To find answer to b) : Determine the time instant when horizontal displacement is 4m. Then determine the vertical displacement (from the top) at that instant. Determine height of the snowball from ground. That will answer b).

Thank you but shouldn't y still equal zero because the y and x-axis is on the bottom of the barn not the roof; even though its traveling negative it hits at zero, not -14?

Never mind, its the same thing. Thank you so much!

 

[Vijay Bhatnagar]

The choice of the origin is optional. You could take the top point as y=0 or the ground as y=0. In the first case initial displacement will be 0 and final displacement -14m. In the second case initial and final displacements will be +14m and 0 respectively. All equations for y-axis will written accordingly.