Question

A stone is thrown vertically upwards with a velocity of 29.4 m/s from the top of a tower 34.3 m high. Find the total time taken by stone to reach the foot of the tower.​

Answer 1

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Note : For seeing diagram need to see via web as picture environment is not working now in app

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Initial thrown velocity of the stone (u) = 29.4 m/s

Height of the tower (h) = 34.3 m

Total time taken to reach the foot of the tower (t) = ? s

Consider AB :

Initial velocity (u) = 29.4 m/s

Final velocity (v) = 0 m/s

Attains rest at maximum height

Acceleration (g) = - 9.8 m/s²

Against the gravity

★ Apply 1st equation of motion ,

➠ v = u + at

➠ 0 = 29.4 + (-9.8)t

➠ 9.8t = 29.4

➠ t = 3 s $\pink{\star}$

★ Apply 3rd equation of motion ,

➠ v² - u² = 2as

➠ (0)² - (29.4)² = 2(-9.8)s

➠ - 864.36 = - 19.6s

➠ s = 44.1 m

Consider BD :

Initial velocity (u) = 0 m/s

Acceleration (g) = 9.8 m/s²

Starts from rest at maximum height

Total height , s' = h + s

➠ s' = 34.3 + 44.1

➠ s' = 78.4 m

Apply 2nd equation of motion ,

➠ s = ut + ¹/₂ at²

➠ 78.4 = (0)t + ¹/₂(9.8)t²

➠ 78.4 = 4.9t²

➠ t² = 16

➠ t = 4 s

Total time = 4 s + 3 s

➠ 7 s