Answer:
a) h = 1/2 gt² b) 99 m/s c) 14.1 m/s
Explanation:
a) As the only force acting on the canister once released is gravity, as it is constant, we can use one of the kinematic equations, as follows:
h = h₀ + v₀t + 1/2a t²
As we are told that the canister is simply released, it means that v₀ =0.
If we choose the direction of the acceleration (downward) as positive ,and we select the height at which it was released as our origin, so h₀ =0, the final expression for height is as follows:
h = 1/2 g t²
b) Combining this equation with the expression of t, from the definition of acceleration as the rate of change of velocity, we arrive to this expression:
vf² - v₀² = 2 g h
As v₀ = 0, we have v₀ = √2.g.h = √2.9.8.500 m²/s² = 99 m/s
c) In order to be able to break the canister, impact speed must be larger than 100 m/s.
So, we can use the same equation as above, putting vf=100 m/s, and solving for v₀, as follows:
v₀² = vf² - 2.g.h = 100² m²/s² - 2.9.8.500 m²/s² = 200 m²/s²
v₀ = √200 m²/s² = 14.1 m/s
For any value of v₀ just barely larger than this, the canister will be broken.
