Projectile Motion Problem

Question

The left field wall in Fenway Park in Boston is 315 ft from home plate and is 37 ft high.

(a) Can a baseball hit with an initial speed of 125 ft/sec clear the wall? What angle is required to do this?

(b) What is the smallest initial velocity that will produce a home run?

Please include any formulas you may use. Thank you.

Answer 1

y = y₀ + (v_θ0sinθ₀)t - 1/2 gt² x = x₀ + (v₀cosθ₀)t x₀ and y₀ = 0

You want to solve for θ₀ , so you you want to do is eliminate t t = x/ (v₀cosθ₀)

y = xtanθ₀ - gx²/(2v₀²cos²θ₀)

Now, it gets a little crazy. 1/cos² = sec² = 1+tan²

y = -gx²/(2v₀²) + x tanθ₀ - gx²/(2v₀²) tan²θ₀

which is a quadratic for tanθ₀ for which you can use the quadratic formula. The tangent solution will give two possible angles if there is a solution. (Any angle between the two angles will work.

This problem is pretty advanced.