A person is driving an automobile at 95 km/h and throws a bottle of mass .600 kg straight out the window. a) With what momentum does the bottle hit the roadway sign? b) With what momentum does the bottle hit an oncoming automobile traveling in the opposite direction at 85 km/h? c) With what momentum does the bottle hit an automobile passing and traveling in the same direction at 115 km/h?
p=m•v
a) v = 95 km/h = 95000/3600 = 26.4 m/s
p = 0.6 • 26.4 = 15.8 kg•m/s
b) v(combined) = 95 + 85 =
26.4+23.6= 50m/s.
p = 50 • 0.6 = 30kg•m/s
c) v(combined)=115 - 95 = 31.9- 26.4
= 5.5 m/s
p= 0.6•5.5 = 3.3 kg•m/s
To solve these problems, we need to convert the speeds from km/h to m/s and use the equation for momentum: momentum = mass * velocity.
a) To calculate the momentum with which the bottle hits the roadway sign, we don't need to consider the velocity of the automobile since the bottle is thrown straight out the window.
Given:
Velocity of the automobile (v) = 95 km/h = 95 * (1000/3600) m/s = 26.39 m/s
Mass of the bottle (m) = 0.600 kg
Using the formula:
Momentum = mass * velocity
Substituting the values:
Momentum = 0.600 kg * 26.39 m/s
Momentum ≈ 15.83 kg·m/s
Therefore, the momentum with which the bottle hits the roadway sign is approximately 15.83 kg·m/s.
b) To calculate the momentum with which the bottle hits the oncoming automobile, we need to consider the velocities of both the bottle and the oncoming automobile.
Given:
Velocity of the automobile (v1) = 85 km/h = 85 * (1000/3600) m/s = 23.61 m/s
Using the formula:
Momentum = mass * velocity
Substituting the values:
Momentum = 0.600 kg * (26.39 m/s + (-23.61 m/s))
Momentum ≈ 1.91 kg·m/s
Therefore, the momentum with which the bottle hits the oncoming automobile is approximately 1.91 kg·m/s.
c) To calculate the momentum with which the bottle hits the passing automobile, we need to consider the velocities of both the bottle and the passing automobile.
Given:
Velocity of the automobile (v2) = 115 km/h = 115 * (1000/3600) m/s = 31.94 m/s
Using the formula:
Momentum = mass * velocity
Substituting the values:
Momentum = 0.600 kg * (26.39 m/s - 31.94 m/s)
Momentum ≈ -3.36 kg·m/s
Note: The negative sign indicates that the momentum is in the opposite direction to the velocity of the bottle.
Therefore, the momentum with which the bottle hits the passing automobile is approximately -3.36 kg·m/s.
To find the momentum of the bottle, we need to use the formula:
Momentum = mass * velocity
a) With what momentum does the bottle hit the roadway sign?
To calculate the momentum of the bottle when it hits the roadway sign, we'll need to find its final velocity. Since it is thrown straight out the window, we can assume its initial velocity is the same as the car's velocity, which is 95 km/h.
First, we need to convert the velocity to meters per second (m/s) because the SI unit for mass is kilograms (kg) and the SI unit for velocity is meters per second.
1 km/h = 1000 m/3600 s = 5/18 m/s
So, the velocity of the car is (95 km/h) * (5/18 m/s) = 26.3889 m/s.
Now, we can calculate the momentum of the bottle:
Momentum = mass * velocity
Given mass = 0.600 kg and velocity = 26.3889 m/s, we have:
Momentum = 0.600 kg * 26.3889 m/s
Therefore, the momentum of the bottle when it hits the roadway sign is 15.8334 kg·m/s.
b) With what momentum does the bottle hit an oncoming automobile traveling in the opposite direction at 85 km/h?
In this case, we have two objects moving in opposite directions. We need to consider their relative velocities.
The velocity of the oncoming automobile is 85 km/h. Since it is traveling in the opposite direction, we can consider its velocity as negative relative to the car throwing the bottle.
So, the relative velocity is (95 km/h) + (-85 km/h) = 10 km/h.
Converting this to m/s, we get:
(10 km/h) * (5/18 m/s) = 2.7778 m/s.
Now, we can calculate the momentum of the bottle when it hits the oncoming automobile:
Momentum = mass * velocity
Given mass = 0.600 kg and velocity = 2.7778 m/s, we have:
Momentum = 0.600 kg * 2.7778 m/s
Therefore, the momentum of the bottle when it hits the oncoming automobile is 1.6667 kg·m/s (rounded to four decimal places).
c) With what momentum does the bottle hit an automobile passing and traveling in the same direction at 115 km/h?
Similar to the previous scenario, we need to consider their relative velocities.
The velocity of the passing automobile is 115 km/h. Since it is traveling in the same direction, we can consider its velocity as positive relative to the car throwing the bottle.
So, the relative velocity is (115 km/h) - (95 km/h) = 20 km/h.
Converting this to m/s, we get:
(20 km/h) * (5/18 m/s) = 5.5556 m/s.
Now, we can calculate the momentum of the bottle when it hits the passing automobile:
Momentum = mass * velocity
Given mass = 0.600 kg and velocity = 5.5556 m/s, we have:
Momentum = 0.600 kg * 5.5556 m/s
Therefore, the momentum of the bottle when it hits the passing automobile is 3.3333 kg·m/s (rounded to four decimal places).