A child boards a bus for summer camp. His mom is waiting next to the bus. The bus begins moving 3 m/s east with respect to the ground. The child is walking 0.5 m/s west towards the back of the bus with respect to the bus. The mother begins running 1 m/s east with respect to the ground, chasing after the bus and thoroughly humiliating her child. What is the child’s velocity
a). relative to the ground?
b). relative to his mother?
relative to ground: 3E+.5W=2.5E
relative to momma: 3E+.5W-1E=1.5E
a). Oh, poor kid, getting thoroughly humiliated by their mom! Anyway, let's get to the answers. To find the child's velocity relative to the ground, we have to add the velocities together. The bus is moving 3 m/s east, and the child is walking 0.5 m/s west. So, the child's velocity relative to the ground is 3 m/s east - 0.5 m/s west, which gives us 2.5 m/s east. That poor child can't catch a break!
b). Now, let's find the child's velocity relative to his mother. Well, his mom is running 1 m/s east, so we subtract that from the child's velocity relative to the ground. That gives us 2.5 m/s east - 1 m/s east, which gives us 1.5 m/s east. So, the child's velocity relative to his mother is 1.5 m/s east. At least the kid is faster than his mom, even if he's being run down!
To determine the child's velocity, we need to consider the velocities of the bus, the child, and the mother.
a) Relative velocity of the child to the ground:
The child's velocity relative to the ground is the combination of the bus's velocity and the child's velocity relative to the bus.
Given:
- Bus velocity relative to the ground = 3 m/s east
- Child's velocity relative to the bus = 0.5 m/s west
The child's velocity relative to the ground is the vector sum of the bus's and child's velocities:
Velocity of the child relative to the ground = Bus velocity + Child's velocity
Velocity of the child relative to the ground = 3 m/s east + (-0.5 m/s west)
Simplifying the equation:
Velocity of the child relative to the ground = 3 m/s - 0.5 m/s
Velocity of the child relative to the ground = 2.5 m/s east
Therefore, the child's velocity relative to the ground is 2.5 m/s east.
b) Relative velocity of the child to his mother:
The relative velocity between the child and his mother is the difference in their velocities.
Given:
- Child's velocity relative to the ground = 2.5 m/s east
- Mother's velocity relative to the ground = 1 m/s east
The relative velocity of the child to his mother is the difference between their velocities:
Relative velocity of the child to his mother = Child's velocity - Mother's velocity
Relative velocity of the child to his mother = 2.5 m/s east - 1 m/s east
Simplifying the equation:
Relative velocity of the child to his mother = 1.5 m/s east
Therefore, the child's velocity relative to his mother is 1.5 m/s east.
To answer these questions, we need to understand the concepts of velocity and relative motion.
Velocity is a vector quantity that describes the rate at which an object changes its position with respect to time. It includes both the speed and direction of an object's motion.
Relative motion refers to the motion of one object with respect to another. It considers the motion of an object relative to a reference frame or observer.
Let's analyze the given scenario step by step to find the answers:
1. The bus is moving 3 m/s east with respect to the ground. The direction is east, and the speed is 3 m/s.
2. The child is walking 0.5 m/s west towards the back of the bus with respect to the bus. Since the child is on the moving bus, we need to consider the child's motion relative to the bus. The direction is west, and the speed is 0.5 m/s.
To find the child's velocity relative to the ground, we need to add the velocities of the child and the bus as vectors because they are moving in different directions. Vector addition involves adding the magnitudes and considering the directions:
Child's velocity relative to the ground = Bus velocity + Child's velocity
Velocity relative to the ground = 3 m/s east - 0.5 m/s west
Velocity relative to the ground = 2.5 m/s east
Hence, the child's velocity relative to the ground is 2.5 m/s east.
3. The mother begins running 1 m/s east with respect to the ground, chasing after the bus. Her direction is east, and the speed is 1 m/s.
To find the child's velocity relative to his mother, we'll consider their relative motion. We'll subtract the mother's velocity from the child's velocity:
Child's velocity relative to his mother = Child's velocity - Mother's velocity
Velocity relative to his mother = 0.5 m/s west - 1 m/s east
Velocity relative to his mother = -0.5 m/s west
Hence, the child's velocity relative to his mother is 0.5 m/s west.
In summary:
a). The child's velocity relative to the ground is 2.5 m/s east.
b). The child's velocity relative to his mother is 0.5 m/s west.