Answer: 22.6 hours
Explanation:
The power is the measure of the rate of energy.
In this problem, the 12.0 V battery is rated at 51.0 Ah, which means it delivers 51.0 A of current in a time of t = 1 h = 3600 s. The power delivered by the battery can be written as
where
I is the current
V = 12.0 V is the voltage of the battery
So the energy delivered by the battery can be written as
Where
So the energy delivered is
At the same time, the headlight consumes 27.0 W of power, so 27 Joules of energy per second; Therefore, it will remain on for a time of:
Answer:
P = 5sin(880πt)
Explanation:
We write the pressure in the form P = Asin2πft where A = amplitude of pressure, f = frequency of vibration and t = time.
Now, striking the middle-A tuning fork with a force that produces a maximum pressure of 5 pascals implies A = 5 Pa.
Also, the frequency of vibration is 440 hertz. So, f = 440Hz
Thus, P = Asin2πft
P = 5sin2π(440)t
P = 5sin(880πt)
When the ball starts its motion from the ground, its potential energy is zero, so all its mechanical energy is kinetic energy of the motion:
where m is the ball's mass and v its initial velocity, 20 m/s.
When the ball reaches its maximum height, h, its velocity is zero, so its mechanical energy is just gravitational potential energy:
for the law of conservation of energy, the initial mechanical energy must be equal to the final mechanical energy, so we have
From which we find the maximum height of the ball:
Therefore, the answer is
yes, the ball will reach the top of the tree.
