Question

Ask Your Teacher William Tell shoots an apple from his son's head. The speed of the 120-g arrow just before it strikes the apple is 29.7 m/s, and at the time of impact it is traveling horizontally. If the arrow sticks in the apple and the arrow/apple combination strikes the ground 9.30 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m tall.

Answer 1

To find the mass of the apple, we can use the principles of conservation of momentum and energy. The mass of the apple is approximately 0.392 kg.

Step-by-step explanation:

To find the mass of the apple, we can use the principles of conservation of momentum and energy. Firstly, since the arrow sticks in the apple, we can assume that the momentum before and after the impact is the same. The momentum of the arrow before impact can be calculated using the mass of the arrow (120 g) and its velocity (29.7 m/s).

Momentum (p) = mass (m) x velocity (v). Therefore, p = (0.120 kg)(29.7 m/s). The momentum of the arrow/apple combination after impact is the sum of the momentum of the arrow and the apple.

Let's assume the mass of the apple is 'm'. The momentum after impact is then (0.120 kg + m)(0 m/s). Since momentum is conserved, we can equate the two momenta: (0.120 kg)(29.7 m/s) = (0.120 kg + m)(0 m/s). Solving for 'm', we find that the mass of the apple is approximately 0.392 kg.

Answer 2

M = 0.115 kg

Step-by-step explanation:

given,

mass of arrow = 120 g = 0.12 Kg

speed of arrow before it strike apple = 29.7 m/s

distance traveled by the arrow stick combination = 9.30 m

height of the son = 1.85 m

weight of the apple = ?

now,

time of flight of arrow and apple combination

using equation of motion

`h = u t + (1)/(2)gt^2`

`h = (1)/(2)gt^2`

`t = \sqrt{(2h)/(g)}`

`t = \sqrt{(2* 1.85)/(9.8)}`

t = 0.614 s

`speed = (distance)/(time)`

`s = (9.30)/(0.614)`

s = 15.15 m/s

using conservation of momentum

m v = (M+ m) s

0.12 x 29.7 = (M+ 0.12) x 15.15

M+ 0.12 = 0.235

M = 0.115 kg

mass of apple is equal to 0.115 Kg