Consider a child standing on a beach who gets hit by a wave. The child weighs 30 kg, and the portion of the wave that hits the child contained 60 kg water. If the wave had a period of 2 seconds and a wavelength of 6 meters, how fast will the child be moving after it is hit by the wave?
This is what I got so far:
v = w/T
v = 6/2
v = 3 m/s
p = m*v
p = 60*3
p = 180 kg m/s
m*v = p
30*v = 180
v = 180/30
v = 60 m/s
But the teacher says it's still wrong, can anyone help? Thanks!
does the water just stop or continue moving with the child?
it it continues moving on the child for an instant, you have 90 kg, not 30
Well, it seems like you're on the right track, but your calculations might be a bit mixed up. Let me give it a shot with a touch of humor:
First, we need to calculate the velocity of the wave using the given formula v = w/T, where w is the wavelength and T is the period. Now, the wavelength is 6 meters, and the period is 2 seconds. So, it's like the wave is telling us, "Hey, I need 2 seconds to complete my fancy dance moves over a distance of 6 meters!" Impressive, wave, impressive.
Now, let's calculate the velocity of this dancing wave. 6 divided by 2 equals... 3 meters per second! Aha! We've got it! The wave is showing off its moves at a speed of 3 meters per second.
But hold on a second, little child on the beach! We need to find out how fast you'll be moving after being hit by this impressive wave. To do that, we'll use the principle of conservation of momentum, which says that the momentum before the wave hits you should be equal to the momentum after the wave hits you.
Now, you weigh 30 kilograms, and the portion of the wave that hits you contains 60 kilograms of water. So, when the wave splashes its water onto you, it's like it's saying, "Oops, sorry! Here's 60 kilograms of momentum for you!"
Now, to find the velocity at which you'll be moving, we multiply the momentum by the mass. So, 60 kilograms of water multiplied by 3 meters per second equals... 180 kilogram meters per second!
And ta-da! Your answer is that you'll be moving at a speed of 180 kilogram meters per second, my little beach buddy. Just make sure to watch out for those dancing waves in the future!
Based on the given information, we can solve the problem using the principle of conservation of momentum. Recall that momentum (p) is given by the equation p = m * v, where m represents mass and v represents velocity.
1. Find the velocity (v) of the wave using the given wavelength (λ) and period (T):
v = λ / T
v = 6 m / 2 s
v = 3 m/s
2. Calculate the initial momentum (p_initial) of the wave before hitting the child:
p_initial = m * v
p_initial = 60 kg * 3 m/s
p_initial = 180 kg m/s
3. Use the principle of conservation of momentum to find the final velocity (v_f) of the child after being hit by the wave. Since the system is initially at rest, the final momentum (p_final) of the child and wave system will be equal to the initial momentum of the wave:
p_final = p_initial
(mass of child) * v_f = 180 kg m/s
(30 kg) * v_f = 180 kg m/s
v_f = 180 kg m/s / 30 kg
v_f = 6 m/s
Therefore, the child will be moving with a velocity of 6 m/s after being hit by the wave.
To find the correct answer, we need to take into account the conservation of momentum before and after the wave hits the child. Let's go through the steps again and break it down:
Step 1: Calculate the velocity of the wave
The formula for the velocity of a wave is v = λ/T, where λ is the wavelength and T is the period.
Given:
λ = 6 meters
T = 2 seconds
v = 6/2 = 3 m/s
So, the velocity of the wave is 3 m/s.
Step 2: Calculate the momentum of the water in the wave
The momentum (p) of an object is given by the formula p = m * v, where m is the mass of the object and v is its velocity.
Given:
m = 60 kg (mass of the water hitting the child)
v = 3 m/s (velocity of the wave)
p = 60 * 3 = 180 kg m/s
So, the momentum of the water hitting the child is 180 kg m/s.
Step 3: Apply the conservation of momentum
According to the law of conservation of momentum, the total momentum before the wave hits the child should be equal to the total momentum after it hits the child.
Given:
Mass of the child = 30 kg (m)
Initial velocity of the child = 0 m/s (u, assuming the child is initially at rest)
Initial momentum before wave hits = m * u
Final momentum after wave hits = (m + 60) * v
So, m * u = (m + 60) * v
Substituting the given values:
(30 * 0) = (30 + 60) * v
0 = 90v
To make this equation true, the velocity (v) of the child after being hit by the wave should be 0 m/s.
Therefore, the correct answer is that the child will not be moving after being hit by the wave. It will remain at rest.