a body is thrown vertically upwards from the top of a tower. It reaches the ground in time t₁. If it is thrown vertically downwards from the top of the tower with the same speed it reaches the ground in time t₂. If it is allowed to fall freely from top of the tower then find the time it takes to reach the ground
Answers
Answer:
√t₁t₂
Explanation:
Let the body be thrown with velocity 'u'(whenever thrown).
Case 1: Thrown upwards
It is thrown upwards with velocity u, states, it is thrown downwards with velocity -u (being a vector),
S = (-u)t₁ + 1/2 gt₁²
S = -ut₁ + 1/2 gt₁² ...(1)
Case 2: Thrown downwards
It is thrown downwards with velocity u,
S = ut₂ + 1/2 gt₂² ...(2)
Case 3: released downwards
It is released downwards it means there is no initial velocity,
S = (0)t₃ + 1/2 gt₃²
√(2S/g) = t₃ ...(3)
Comparing (1) and (2), we get
⇒ -ut₁ + 1/2 gt₁² = ut₂ + 1/2 gt₂²
⇒ 1/2 g(t₁ - t₂) = u
Substituting this in (1), we get
⇒ S = -1/2 g(t₁ - t₂)t₁ + 1/2 gt₁²
S = 1/2 gt₁t₂
Substitute this in (3), we get
t₃ = √(2 * 1/2 gt₁t₂ / g)
t₃ = √t₁t₂
The time taken to reach the ground(when released) is √t₁t₂
Explanation:
topic :
- time and speed
to find :
- find the time it takes to reach the ground
let us do :
- please check the attached file where your answer
