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sesenic [268]
3 years ago
8

A dynamite blast at a quarry launches a rock straight upward, and 1.7 s later it is rising at a rate of 17 m/s. Assuming air res

istance has no effect on the rock, calculate its speed (a) at launch and (b) 4.9 s after launch.
Physics
1 answer:
Shtirlitz [24]3 years ago
3 0

Answer:

(a) v_0= 34m/s

(b) v=14m/s

Explanation:

We can derive the initial speed of the rock from the equation of the speed in function of the time:

v=v_0-gt\\\\\implies v_0=v+gt

Using the given values for the speed at time t=1.7s, we get:

v_0=17m/s+(9.8m/s^{2})(1.7s)=34m/s

In words, the speed of the rock at launch is 34m/s (a).

Next, we use this to calculate the speed at t=4.9s:

v=v_0-gt\\\\v= 34m/s-(9.8m/s^{2})(4.9s)=-14m/s

This means that the speed of the rock at 4.9s after the launch is 14m/s (b), and the negative sign means that it is moving downwards.

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<u>Conservation of Momentum </u>

The total momentum of a system of two particles is

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Where m1,m2,v1, and v2 are the respective masses and velocities of the particles at a given time. Then, the two particles collide and change their velocities to v1' and v2'. The final momentum is now

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The momentum is conserved if no external forces are acting on the system, thus

m_1v_1+m_2v_2=m_1v_1'+m_2v_2'

Let's put some numbers in the problem and say

m_1=8\ kg,\ m_2=6\ kg,\ v_1=12\ m/s, v_2=4\ m/s,\ v_1'=-6\ m/s,\ v_2'=28\ m/s

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96+24=-48+168

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It means that when the particles collide, the first mass returns at 6 m/s and the second continues in the same direction at 28 m/s

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