Two bodies fall from a height of 20 m. Without initial velocity. One of them meets a platform inclined at an angle of 45. The impact point is at a height of 10 m. Is it necessary to determine the fall time of the bodies t1 and t2?
When the first body hits the platform, the angle of incidence will be equal to the angle of reflection. Immediately after the impact, the body will have only a horizontal velocity component.
The vertical component is v₀ = 0.
It can be assumed that the body fell 2 times from a height of h₁ = 10 m. The total time of the body falling t₁ is equal to twice the time of falling t from a height of h₁ = 10 m.
h₁ = gt² / 2.
2h₁ = gt².
t = root (2h₁ / g);
t = root ((2 * 10 m) / 9.8 m / s²) = 1.42 s;
t₁ = 2t = 2.84 s.
Fall time of the second body:
h₂ = 20 m; t₂ = root (2h₂ / g) = ((2 * 20 m / 9.8 m / s²) = 4.08 s.
Answer: t₁ = 2.84 s, t₂ = 4.08 s.
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