It is a curious math problem, which you can prove, that snowballs thrown (45+-Theta) will land at the same place.
so if one is 75 deg, the other must be thrown at 15 deg (45+-30deg)
Does that help?
so if one is 75 deg, the other must be thrown at 15 deg (45+-30deg)
Does that help?
y = (v0y * t) + (1/2 * a * t^2)
Where:
- y is the vertical displacement of the snowball (in this case, we assume it reaches the same height as the second snowball when it is thrown).
- v0y is the initial vertical velocity (which can be calculated as v0 * sinθ, where v0 is the initial speed and θ is the launch angle).
- a is the acceleration due to gravity (-9.8 m/s^2).
- t is the time.
Since both snowballs are thrown with the same speed and the first one is thrown at a 75.0° angle, we can calculate the initial vertical velocity (v0y) as:
v0y = v0 * sinθ
v0y = 30.0 m/s * sin(75.0°)
Using a scientific calculator, we find that v0y ≈ 30.0 * 0.966 = 28.98 m/s.
Now, we can use the kinematic equation to solve for time:
0 = (28.98 * t) + (1/2 * -9.8 * t^2)
Simplifying the equation, we get:
-4.9t^2 + 28.98t = 0
Now, we can factor out t:
t(28.98 - 4.9t) = 0
This equation has two solutions: t = 0 (which doesn't make sense in this context) and 28.98 - 4.9t = 0. Solving for t, we get:
28.98 - 4.9t = 0
4.9t = 28.98
t ≈ 5.92 seconds
Therefore, we should throw the second snowball approximately 5.92 seconds after the first one is thrown.