(a) The landing speed of snowball A is the same as the landing speed of snowball B. This is because the horizontal component of the velocity does not affect the vertical motion of the snowball, and both snowballs are thrown with the same initial vertical velocity.
When snowball A is thrown straight downward, its initial velocity is purely vertical with a magnitude of 13 m/s (assuming no air resistance). The horizontal component of its velocity is zero.
When snowball B is thrown at an angle of 25° above the horizontal, its initial velocity can be broken down into horizontal and vertical components. The vertical component is given by 13 m/s * sin(25°), and the horizontal component is given by 13 m/s * cos(25°). The vertical component determines the initial vertical velocity of snowball B, which is the same as snowball A's vertical velocity.
(b) To calculate the landing speed of both snowballs, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (landing speed)
u = initial velocity
a = acceleration (gravity, approximately 9.8 m/s²)
s = displacement (vertical distance fallen, 7.0 m)
For both snowballs A and B, the initial vertical velocity (u) is 13 m/s.
For snowball A:
The vertical acceleration (a) is -9.8 m/s² (negative because it's acting in the opposite direction to the initial velocity).
The vertical displacement (s) is 7.0 m.
Using the equation:
v^2 = (13 m/s)^2 + 2 * (-9.8 m/s²) * 7.0 m
v^2 = 169 m²/s² - 137.2 m²/s²
v^2 = 31.8 m²/s²
Taking the square root of both sides to find the landing speed (v):
v = √(31.8 m²/s²) ≈ 5.64 m/s
For snowball B:
The vertical acceleration (a) is -9.8 m/s² (same as before).
The vertical displacement (s) is also 7.0 m (same as before).
Using the equation:
v^2 = (13 m/s * sin(25°))^2 + 2 * (-9.8 m/s²) * 7.0 m
v^2 = (13 m/s * 0.4226)^2 - 137.2 m²/s²
v^2 = 11.01 m²/s² - 137.2 m²/s²
v^2 = -126.19 m²/s²
The result is negative, which indicates that the snowball B will never reach the ground. This makes sense because the snowball B was launched at an angle above the horizontal, and its vertical velocity is not sufficient to overcome the initial upward motion. Therefore, snowball B does not land, and its speed cannot be calculated.
In conclusion, the landing speed of snowball A is approximately 5.64 m/s, and snowball B does not land. The assumption that the landing speed of snowball A is the same as snowball B is verified by the calculation.