You are sitting in a car going 20 m/s relative to the ground and decide to throw a ball backwards with a velocity of 4m/s relative to your car. A person in another car behind you sees the ball moving towards him with a velocity of 2.50 m/s relative to his car. What is the velocity of the second car?
My Work:
20/4 = x/2.5
x = 12.5
Is this correct?
suppose an observer were sitting still directly behind you. He would see the ball receding at 20-4 = 16 m/s.
Instead, he sees the ball approaching at 2.5 m/s. So, his velocity is 16+2.5 = 18.5 m/s in your direction.
What's with the ratios? We're not talking about casting shadows here.
oooo I see thank you so much, I just figured that the ratio of the car1 to the ball would equal the ratio of the car2 to the ball for some reason but this makes so much sense ! much appreciated!!!
Yes, your approach to solving the problem is correct. Let's break it down step by step:
First, let's define the velocities:
- You are sitting in a car moving at 20 m/s relative to the ground (velocity of the first car).
- You throw a ball backwards with a velocity of 4 m/s relative to your car.
- The person in the second car sees the ball moving towards them with a velocity of 2.50 m/s relative to their car.
Now, in order to find the velocity of the second car, we can use the principle of relative velocities. We just need to set up an equation using the given information.
The velocity of the ball relative to the ground can be calculated by adding the velocity of the first car (20 m/s) to the velocity of the ball relative to the car (4 m/s).
So, the velocity of the ball relative to the ground is 20 m/s + 4 m/s = 24 m/s.
Now, we can set up the equation using the principle of relative velocities:
Velocity of the ball relative to the second car = Velocity of the ball relative to the ground - Velocity of the second car.
Substituting the known values:
2.50 m/s = 24 m/s - Velocity of the second car.
To solve for the velocity of the second car, rearrange the equation:
Velocity of the second car = 24 m/s - 2.50 m/s = 21.50 m/s.
Therefore, the velocity of the second car is 21.50 m/s.