A 75 kg soccer player jumps vertically upwards and heads the 0.45 kg ball as it is descending vertically with a speed of 24 m/s.
1 answer:
Answer:
31.66 m/s
Explanation:
mass of player, M = 75 kg
mass of ball, m = 0.45 kg
initial velocity of player, U = + 4 m/s
initial velocity of ball, u = - 24 m/s
Let the final speed of player is V and the ball is v.
use conservation of momentum
Momentum before collision = momentum after collision
75 x 4 - 0.45 x 24 = 75 x V + 0.45 x v
289.2 = 75 V + 0.45 v .... (1)
As the collision is perfectly elastic, coefficient of restitution,e = 1
So,
V - v = u - U
V - v = -24 - 4 = - 28
V = v - 28, put this value in equation (1), we get
289.2 = 75 (v - 28) + 045 v
289.2 = 75 v - 2100 + 0.45 v
2389.2 = 75.45 v
v = 31.66 m/s
Thus, the velocity of ball after collision is 31.66 m/.
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(1)
where
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At time t=0,
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(b) On the coil: 0 V, on the resistor: 20 V
Here we are analyzing the situation several seconds later, which means that we are analyzing the situation for
Since is at the order of less than milliseconds.
Using eq.(1), we see that for , the exponential becomes zero, and therefore the potential difference across the coil is zero:
Therefore, the potential difference across the resistor will be
(c) Yes
The two voltages will be equal when:
(2)
Reminding also that the sum of the two voltages must be equal to the voltage of the battery:
And rewriting this equation,
Substituting into (2) we find
So, the two voltages will be equal when they are both equal to 10 V.
(d) at
We said that the two voltages will be equal when
Using eq.(1), and this last equation, this means
And solving the equation for t, we find the time t at which the two voltages are equal:
(e-a) -19.2 V on the coil, 19.2 V on the resistor
Here we have that the current in the circuit is
The problem says this current is stable: this means that we are in a situation in which , so the coil has no longer influence on the circuit, which is operating as it is a normal circuit with only one resistor. Therefore, we can find the potential difference across the resistor using Ohm's law
Then the battery is removed from the circuit: this means that the coil will discharge through the resistor.
The voltage on the coil is given by
(1)
which means that it is maximum at the moment when the battery is disconnected, when t=0:
And V this time is the voltage across the resistor, 19.2 V (because the coil is now connected to the resistor, not to the battery). So, the voltage across the coil will be -19.2 V, and the voltage across the resistor will be the same in magnitude, 19.2 V (since the coil and the resistor are connected to the same points in the circuit): however, the signs of the potential difference will be opposite.
(e-b) 0 V on both
After several seconds,
If we use this approximation into the formula
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We find that
And since now the resistor is directly connected to the coil, the voltage in the resistor will be the same as the coil, so 0 V. This means that the coil has completely discharged, and current is no longer flowing through the circuit.