Answer:
C. 30 years
Explanation:
Half life of a radioactive substance is defined as the time taken by the substance to decay to half of its original value.
The number of days it will take for one half of the original amount of a radioactive substance to decay given the half life of 30 years will be that same 30years according to the half life definition.
According to the formula for half life t1/2 = ln2/¶ where ¶ is the decay constant.
¶ = ln2/t1/2
¶ = ln2/30
¶ = 0.023
Using the radioactivity formula to get the time it will take 1/2 of the original amount to decay, we have;
N/No = e^-¶t where
N/No is the fraction of amount decayed at time t i.e 1/2
Substituting the given values in the equation, we have;
1/2 = e^-0.023t
ln1/2 = lne^-0.023t
ln1/2 = -0.023t
t = ln0.5/-0.023
t = 30years.
B. velocity only
C. temperature only
D. mass and velocity
(b) After Mike opens his parachute, he continues to descend, eventually reaching the ground with a speed of 4.0 m/s. Calculate the average upward force during this part of Mike's descent.
(c) At the same time Mike jumps out of the airplane, his wallet (mass of 0.3 kg) falls out of his pocket. Calculate the wallet's downward speed when it reaches the ground. For this calculation, assume that air resistance is negligible.
The average magnitude of the upward force of air resistance on Mike during his initial descent is 0 N. The average upward force during the descent after Mike opens his parachute is 1.552 N. The downward speed of the wallet when it reaches the ground is 196.196 m/s.
(a) Average magnitude of the upward force of air resistance:
To find the average magnitude of the upward force of air resistance during Mike's initial descent, we need to calculate the net force acting on him. This can be done by subtracting his weight from the gravitational force:
Net force = gravitational force - weight
Gravitational force = mass * acceleration due to gravity = 97 kg * 9.8 m/s2 = 950.6 N
Weight = mass * acceleration due to gravity = 97 kg * 9.8 m/s2 = 950.6 N
Net force = 950.6 N - 950.6 N = 0 N
Since the net force is 0 N, the average magnitude of the upward force of air resistance is also 0 N.
(b) Average upward force after opening parachute:
When Mike opens his parachute, air resistance plays a significant role in slowing him down. The average upward force can be calculated using the equation:
Average upward force = mass * acceleration
Acceleration = (final speed - initial speed) / time
Time = distance / (final speed - initial speed)
Acceleration = (4.0 m/s - 68 m/s) / (1000 m / (4.0 m/s - 68 m/s)) = 0.016 m/s2
Average upward force = 97 kg * 0.016 m/s2 = 1.552 N
(c) Speed of the wallet:
Since the wallet has negligible air resistance, we can use the equation for freefall to calculate its speed:
Final speed = initial speed + acceleration * time
Acceleration = acceleration due to gravity = 9.8 m/s2
Time = sqrt(2 * height / acceleration) = sqrt(2 * 2000 m / 9.8 m/s2) = 20.02 s
Initial speed = 0 m/s
Final speed = 0 m/s + 9.8 m/s2 * 20.02 s = 196.196 m/s
Therefore, the downward speed of the wallet when it reaches the ground is 196.196 m/s.
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The force of air resistance on Mike during his initial descent and after opening his parachute is approximately 950.6 N. Ignoring air resistance, his wallet will reach the ground at approximately 198 m/s.
The subject of this question is Physics, and it requires understanding of forces and kinematics to apply to the real world scenario of skydiving.
During the initial descent, Mike doesn't have a parachute open. So, the only forces at play initially are his weight and the force of air resistance. We know that he achieves a steady speed of 68 m/s, which means the forces are balanced (net force is zero). Since weight and air resistance counterbalance each other, we calculate the weight by multiplying mass (97 kg) by acceleration due to gravity (9.8 m/s2), which yields 950.6 N. Given the forces balance, this is also the force of air resistance and the answer to part (a).
After the parachute opens, Mike continues to descend, eventually reaching the ground with a speed of 4.0 m/s, indicating a different balance between weight and airresistance. The weight remains the same, but the air resistance (upward force) has increased and once again equals weight since there is no acceleration. Hence, the upward force is still 950.6 N.
For the wallet, we're told to ignore air resistance. So, it's a free fall scenario. We can use the equation of motion v2 = u2 + 2gs to calculate the final speed. Initial speed (u) is 0, g is 9.8 m/s2 and s (displacement) is 2000 m. Substituting these values in, we calculate a final speed of approximately 198 m/s.
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