The tennis ball is thrown vertically at a speed of V0. Is it possible to select such a speed that

| May 23, 2021 | education

The tennis ball is thrown vertically at a speed of V0. Is it possible to select such a speed that, moving vertically upward, the ball would rise in 2 seconds to a height of 10m?

Task data: t (ascent duration) = 2 s; h (required height) = 10 m.

Constants: g (acceleration due to gravity) ≈ 10 m / s2.

Method 1) The initial speed of a tennis ball under the given conditions: S = h = V0 * t – g * t ^ 2/2, whence V0 = (h + g * t ^ 2/2) / t = (10 + 10 * 2 ^ 2/2) / 2 = 15 m / s.

Final speed at a height of 10 m: V = V0 – g * t = 15 – 10 * 2 = -5 m / s (incorrect).

Method 2) Minimum throw speed: h = S = V02 / 2g, whence V0 = √ (2g * h) = √ (2 * 10 * 10) = 14.14 m / s.

Maximum ascent duration: t = V / g = 14.14 / 10 = 1.414 s <2 s.

Answer: There is no initial speed at which a tennis ball rises to a height of 10 m in 2 seconds.



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