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Answer to Question #11461 in Mechanics | Relativity for Ankit

Question #11461
The ceiling of a long hall is 25m high.What is the maximum horizontal distance that a ball thrown with a speed of 40ms-1 can go without hitting the ceiling of the hall ?
Expert's answer
hmax = 25 m
hmax = V0y * t - g * t^2 / 2, t = V0y / g, V0y = V0 *
sinA
hmax = V0^2 * (sinA)^2 / g - (g / 2) * V0^2 * (sinA)^2 / g^2
hmax =
V0^2 * (sinA)^2 / g - V0^2 * (sinA)^2 / (2 * g) = V0^2 *
(sinA)^2 / (2 *
g)
25 = (sinA)^2 * 40^2 / (9.81 * 2)
sinA = sqrt(25 * 9.81 * 2 / 1600) =
0.5537
A = 33.62 degrees

lmax = V0x * t, t = V0y / g, V0x = V0 * cosA,
V0y = V0 * sinA
lmax = V0 * cosA * V0 * sinA / g = 40 * 40 * 0.8327 * 0.5537
/ 9.81 =
[approx.] = 75 m

Answer: 75 m.

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