Question

A snowball rolls off a barn roof that slopes downward at an angle of α= 45.0∘...


A snowball rolls off a barn roof that slopes downward at an angle of α= 45.0∘ . (See the figure below) The edge of the roof is H= 17.0 m above the ground, and the snowball has a speed of v = 4.00 m/s

as it rolls off the roof. Ignore air resistance.

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

Homework Answers

Answer #1

Solution-

Using the formula

Y = VyT + (1/2)gT^2

here

Y is the vertical distance that snowball has to fall = 17m
Vy is the vertical component of the initial velocity = 4.00(sin 45)

= 2.83 m/sec.
T is the time for the snowball to hit the ground
g (acceleration due to gravity) = 9.8 m/sec^2

Substituting the values,

17 = 2.83T + (1/2)(9.8)T^2

17 = 2.83 T + 4.9T^2

4.9T^2 + 2.83T - 17 = 0

Solving the quadratic equation,

T = 1.596 sec.

Now using formula
X = Vx(T)

here

X is the distance from the edge of the barn where the snowball will land
Vx is the horizontal component of the initial velocity = 4(cos 45)

= 2.83 m/sec.
T = 1.596 sec
Substituting values,

X = 2.83 * 1.596

X = 4.52 meters

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