A 1230 kg car drives along a city street at 31.0 miles per hour, and a baseball has a mass of 0.142 kg. What speed must the baseball have if its momentum is to be equal in magnitude to that of the car? Give your result in miles per hour.
m1v1=m2v2
You have mass and velocity of car (lets designate that m1 and v1) and mass of ball (lets say that's m2). Solve for v2.
Well, I'm not a physicist, but let's give this a shot anyway. If the momentum of the baseball is equal to that of the car, then we can use the equation p = mv, where p is the momentum, m is the mass, and v is the velocity.
First, let's find the momentum of the car. Since the car has a mass of 1230 kg and is traveling at 31.0 mph, we can calculate its momentum as:
momentum of car = (1230 kg)(31.0 mph) = 38,130 kg*mph
Now, we can use this momentum to find the velocity of the baseball. Since momentum is calculated as p = mv, we can rearrange the equation to solve for velocity:
v = p / m
Plugging in the values, we get:
v = (38,130 kg*mph) / (0.142 kg) = 268,591.5 mph
So, to have momentum equal in magnitude to that of the car, the baseball would need to be traveling at approximately 268,591.5 mph.
Now, this seems a bit unrealistic for a baseball, so I think we might have gone wrong somewhere along the way. But hey, who knows, maybe baseballs are faster than we thought!
To find the speed of the baseball, we can use the equation for momentum:
Momentum = mass * velocity
We know the momentum of the car, so let's find the momentum first.
Momentum of the car = mass of the car * velocity of the car
Momentum of the car = 1230 kg * 31.0 miles per hour
Now, let's calculate the momentum of the car.
Momentum of the car = 38130 kg * miles per hour
Next, we want the momentum of the baseball to be equal in magnitude to that of the car. The magnitude of momentum is always positive, so we don't have to worry about the negative sign.
Momentum of the baseball = Momentum of the car
mass of the baseball * velocity of the baseball = 38130 kg * miles per hour
Now, let's solve for the velocity of the baseball.
velocity of the baseball = (mass of the car * velocity of the car) / (mass of the baseball)
velocity of the baseball = (1230 kg * 31.0 miles per hour) / 0.142 kg
Finally, let's calculate the velocity of the baseball.
velocity of the baseball = 268838.02817 miles per hour
Therefore, the speed of the baseball must be approximately 268,838.03 miles per hour to have the same magnitude of momentum as the car.
To find the speed of the baseball, we need to know the momentum of the car and then set it equal to the momentum of the baseball.
First, let's find the momentum of the car.
Momentum (p) is calculated using the formula:
p = mass × velocity
Given:
Mass of the car (m₁) = 1230 kg
Velocity of the car (v₁) = 31.0 miles per hour
Using the formula, we can calculate the momentum of the car:
p(car) = m₁ × v₁
p(car) = 1230 kg × 31.0 miles per hour
However, the units of mass are in kg, and the units of velocity are in miles per hour. To perform the calculation correctly, we need to convert the velocity from miles per hour to meters per second.
1 mile per hour is equal to 0.44704 meters per second.
v₁ = 31.0 miles per hour × 0.44704 meters per second / 1 mile per hour
v₁ = 13.84864 meters per second
Let's substitute this value back into the momentum equation:
p(car) = 1230 kg × 13.84864 meters per second
p(car) ≈ 17019.7952 kg·m/s
Now, we need to find the speed of the baseball by setting its momentum equal to the momentum of the car.
Using the same momentum formula, we have:
p(baseball) = m₂ × v₂
Given:
Mass of the baseball (m₂) = 0.142 kg
To find the velocity (v₂) of the baseball, we set the momentum of the baseball equal to the momentum of the car:
p(baseball) = p(car)
m₂ × v₂ = 17019.7952 kg·m/s
Solving for v₂, we have:
v₂ = 17019.7952 kg·m/s / 0.142 kg
v₂ ≈ 119880.5641 meters per second
Finally, we convert this result back into miles per hour:
v₂ = 119880.5641 meters per second × 2.23694 miles per hour / 1 meter per second
v₂ ≈ 267940.7447 miles per hour
Therefore, the speed at which the baseball must travel to have the same momentum as the car is approximately 267940.7447 miles per hour.