What is the distance of a car travels is its velocity is 30 mph and its time is 2 hours ?
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Answer:
v₀ = 240 m / s
Explanation:
This problem must be solved in two parts, first we must use the conservation of the moment, then the conservation of energy.
Let's start by applying moment conservation, to the system formed by the block and bullet, in this case the forces during the crash are internal and the moment is conserved
Instant starts. Before the crash
p₀ = m v₀
Final moment. Right after the crash
= (m + M) v
The moment is preserved
Po =p_{f}
M v₀ = (m + M) v
v = m / (m + M) v₀ (1)
This is the speed with which the bullet block system comes out, now we can use energy conservation
Starting point. Right after the crash
Em₀ = K = ½ (m + M) v²
Final point. Highest point of the path
= U = (m + M) g y
Em₀ = Em_{f}
½ (m + M) v² = (m + M) g y
v = √2 g y (2)
We substitute 1 in 2
m / (m + M) v₀ = √ 2gy
v₀ = (m + M) / m √ 2gy
Let's calculate
v₀ = (0.0134 +0.800) /0.0134 √ (2 9.8 0.8)
v₀ = 240 m / s