Projectile motion problem

Question

A shot-putter throws the shot mass=7.3kg with an initial speed of 14.4m/s at angle 34 degrees with horizontal.Calculate the horizontal distance travelled by the shot if it is leaves the athlete's hand at height of 2.10m above the ground.

Answer 1

The shot height depends on time like y = y₀ + st sinθ – gt²/2 so by the quadratic formula, it reaches y → 0 at t → (s sinθ + √(s²sin²θ + 2gy₀))/g. The range is then x = st cosθ.