Let's discuss the beautiful snowball problem useful for Physics Olympiad.
The Snowball Problem:
(a) A snowball rolls off a barn roof that slopes downward at an angle of \(40^\circ\). The edge of the roof is 14.0m above the ground and the snowball has a speed of 7.00m/s as it rolls off the roof. 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 1.9m tall is standing 4.0m from the edge of the barn. Will he be hit by the snowball?
Solution:
The snowball follows the projectile motion.
In part(a), the vertical motion determines the time in the air.
The acceleration $$a_x=0$$, $$a_y=+9.80m/s^2$$ and $$v_x=v_0cos\theta_0=7cos40^\circ=5.36m/s$$
Vertical component of velocity $$ v_y=v_0sin\theta_0=4.50m/s$$
Now, distance from ground \(s=14m\).
$$ 14=(4.50)t+(\frac{1}{2}\times9.8\times t^2)$$
We use Sreedhar-Acharya's method to solve for t.
$$ t=\frac{(-4.5 \pm \sqrt{4.5^2-4(4.9)(-14)}}{2(4.9))}$$
The positive root for \( t=1.29s\)
The horizontal distance$$ v_xt+(1/2)a_x t^2= 6.91m$$
(b) $$ x-x_0=v_xt+\frac{1}{2}a_xt^2$$ gives $$ t=\frac{x-x_0}{v_x}=\frac{4.0}{5.36}=0.746s$$ In this time the snowball travels downward a distance $$ y-y_0=v_y+\frac{1}{2}a_y t^2=6.08m$$ and is therefore
$$ 14.0-6.08=7.9m$$ above the ground. The snowball passes well above the man and does not hit him.
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]