Solving Physics Mechanics Problem: Snowball Off Barn Roof

In summary, a snowball rolls off a barn roof that slopes downward at an angle of 40 degrees. The edge of the roof is 14.0 meters above the ground, and the snowball has a speed of 7.00 meters per second when it rolls off the roof. If the snowball doesn't strike anything else while falling, it will strike the ground at a distance of 10.4 meters from the barn. If a man 1.9 meters tall is standing 4.0 meters from the edge of the barn, he will be hit by the snowball. The formulas for velocity and distance when objects have acceleration (in this case acceleration due to gravity) can be used to determine the height of the snowball when the distance from the barn is 4.
  • #1
Tony Zalles
22
0
Ok so I'm havin just a bit of trouble with this problem...

ok here it is.

A snowball rolls off a barn roof that slopes downward at an angle of 40 Degrees. The edge of the roof is 14.0 m above the ground, and the snowball has a speed of 7.00 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 srike anything else while falling?

B)A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?

Part A: ok this was easy I got this:

tan (40 degrees) = X/15

X ≈ 11.75 m

(X = distance from the edge of the barn to where the snowball strikes the ground)

Part B: I'm stumped here I'm not even sure what approach to take...

I'm guessing I have to caculate the path of the snowball. And see if it hits him. (I'm not sure how to do this I'm guessing using (1/2at^2+Vit+Xi)

(i = initial)


Any help would be appreciated thanks. :)
 
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  • #2
Part A: ok this was easy I got this:

tan (40 degrees) = X/15

X ¡Ö 11.75 m
Apparently it wasn't easy enough. You are assuming the snowball continued in a straight line after leaving the roof. It doesn't happen that way. Things FALL!

Do you know the formulas for velocity and distance when objects have acceleration (in this case acceleration due to gravity)?
The snowball will hit about 10.4 meters from the barn. Can you see how to get that?
Give it a try and get back to us.

b) Use the same formulas you did in a) to determine the height of the snowball when the distance from the barn is 4.0 m. Does the snowball pass over the man or hit him?
 
  • #3
err...yea that was careless of me well ok so after lookin at it again I got this.

A snowball rolls off a barn roof that slopes downward at an angle of 40 Degrees. The edge of the roof is 14.0 m above the ground, and the snowball has a speed of 7.00 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 srike anything else while falling?

B)A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?

Vx = (Vo)(cos θ), Vx ≈ 5.36 m/s
Vy = (Vo)(sin θ), Vy ≈ 4.50 m/s

Ok now I need to find the horizontal distance

Vo = 7 m/s
Xo = 14 m
a = -9.8 m/s^2

Y = Xo + Vot + (1/2)(a)(t)^2
t ≈ 2.55 s

V(t) = at + vo
V(t) ≈ -17.98 m/s

5.36m ≈ X/2.55s

x ≈ 13.67 m

Thats what I got I'm not all that sure if I'm right.

And so for part B I think I have to use this equation but well...man i', still kind of confused about which equation(s) to plug in the variables 1.9 m and 4.0 m to determine if he gets hit.

Y = Xo + Vot + (1/2)(a)(t)^2

(hey thanks for helpin me get started HallsofIVY)

Any help is appreciated.
 

1. What is the initial velocity of the snowball?

The initial velocity of the snowball can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time. The initial velocity can also be determined by measuring the height of the barn roof and the angle at which the snowball is thrown.

2. How long will it take for the snowball to hit the ground?

The time it takes for the snowball to hit the ground can be calculated using the equation t = √(2h/g), where t is the time, h is the height of the barn roof, and g is the acceleration due to gravity. This equation assumes that the snowball is thrown from the edge of the roof and that air resistance is negligible.

3. What factors affect the trajectory of the snowball?

The trajectory of the snowball can be influenced by several factors, including the initial velocity, the angle at which it is thrown, and air resistance. The height and shape of the barn roof can also impact the trajectory. Additionally, external forces such as wind can affect the path of the snowball.

4. How does the mass of the snowball affect its motion?

The mass of the snowball does not significantly affect its motion if air resistance is negligible. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. However, in this scenario, the force of gravity is the same for all objects regardless of their mass, so the acceleration due to gravity is constant.

5. What is the maximum distance the snowball can travel?

The maximum distance the snowball can travel is determined by its initial velocity and the angle at which it is thrown. The horizontal distance traveled can be calculated using the equation d = v0 * cosθ * t, where d is the distance, v0 is the initial velocity, θ is the angle of projection, and t is the time. The maximum distance will be achieved when the angle of projection is 45 degrees.

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