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EleoNora [17]
3 years ago
5

A rock is thrown upward with a velocity of 23 meters per second from the top of a 25 meter high cliff, and it misses the cliff o

n the way back down. when will the rock be 11 meters from the water, below
Physics
1 answer:
Nana76 [90]3 years ago
8 0
Vf=vi+at
-23m/s=23m/s-9.8m/s^2(t)
t1 from throwing up back to starting position t1=4.693s
Delta(x)=vi(t)+.5a(t^2)
25-11=14
-14m=-23m/s(t)-4.8m/s^s(t^2)
t2 is from 25m to 11 m t2=.546s
Total time =5.239s
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the acceleration a^{\to} = (0.0159 \ \ m/s^2 )i

Explanation:

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the initial speed v₁ = 0 m/s i.e starting from rest ; since the car accelerates at a distance Δx = 6 miles in order to teach that final speed v₂ of 63.15 km/h.

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v₂² = v₁² + 2a (Δx)

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v₂² - v₁² = 2a (Δx)

a = \dfrac{v_2^2 - v_1^2 }{2 \Delta x}

a = \dfrac{(63.15 \ km/s)^2 - (0 \ m/s)^2 }{2 (6 \ miles)}

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2.09\ \text{m/s}

22298.4\ \text{J}

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u_2 = Initial velocity of the other two cars = 1.4 m/s

v = Velocity of combined mass

As the momentum is conserved in the system we have

mu_1+2mu_2=3mv\\\Rightarrow v=\dfrac{u_1+2u_2}{3}\\\Rightarrow v=\dfrac{3.46+2\times 1.4}{3}\\\Rightarrow v=2.09\ \text{m/s}

Speed of the three coupled cars after the collision is 2.09\ \text{m/s}.

As energy in the system is conserved we have

K=\dfrac{1}{2}mu_1^2+\dfrac{1}{2}2mu_2^2-\dfrac{1}{2}3mv^2\\\Rightarrow K=\dfrac{1}{2}\times 1.6\times 10^4\times 3.46^2+\dfrac{1}{2}\times 2\times 1.6\times 10^4\times 1.4^2-\dfrac{1}{2}\times 3\times 1.6\times 10^4\times 2.09^2\\\Rightarrow K=22298.4\ \text{J}

The kinetic energy lost during the collision is 22298.4\ \text{J}.

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