while sitting on a tree branch 10 m above the ground, you drop a chestnut. When the chestnut has fallen 2.5 m, you throw a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time?

Question

Marin Combs

Physics

21 November, 22:42

while sitting on a tree branch 10 m above the ground, you drop a chestnut. When the chestnut has fallen 2.5 m, you throw a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time?

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Answers (1)

Know the Answer?

Chaim Roman · Answer 1

10.5 m/s

Explanation:

For the first chestnut:

y₀ = 10 m

v₀ = 0 m/s

a = - 9.8 m/s²

y = y₀ + v₀ t + ½ at²

y = 10 + (0) t + ½ (-9.8) t²

y = 10 - 4.9t²

When y = 7.5:

7.5 = 10 - 4.9t²

t = 5/7

When y = 0:

0 = 10 - 4.9t²

t = 10/7

For the second chestnut:

y₀ = 10 m

y = 0 m

a = - 9.8 m/s²

t = 10/7 s - 5/7 s = 5/7 s

y = y₀ + v₀ t + ½ at²

0 = 10 + v₀ (5/7) + ½ (-9.8) (5/7) ²

0 = 10 + 5/7 v₀ - 2.5

v₀ = - 10.5

The second chestnut must be thrown downwards at 10.5 m/s.