Question

White standing on a tree branch 10.0m above the ground you drop a chestnut. When the chestnut has fallen 2.5m, you throw a second chestnut straight down. (a) What velocity does the first chestnut have after it has dropped 2.5m? (b) How long does it take the first chestnut to fall the last 7.5m? (c) What initial speed must you give the second chestnut if they are both to reach the ground at the same time.

Answer 1

a) 7.07 m/s

b) 0.707 s

c) 10.6 m/s

Step-by-step explanation:

Take down to be positive.

a) Given for the first chestnut:

s = 2.5 m

u = 0 m/s

a = 10 m/s²

Find: v

v² = u² + 2as

v² = (0)² + 2(10)(2.5)

v = 7.07 m/s

b) Given for the first chestnut after falling 2.5 m:

s = 7.5 m

u = 7.07 m/s

a = 10 m/s²

Find: t

s = u t + ½ a t²

7.5 = (7.07) t + ½ (10) t²

t = 0.707 s

c) Given for the second chestnut:

s = 10.0 m

a = 10 m/s²

t = 0.707 s

Find: u

s = u t + ½ a t²

10.0 = u (0.707) + ½ (10) (0.707)²

u = 10.6 m/s