A person riding in the back of a pickup truck traveling at 60km/h on a straight, level road throws a ball with a speed of 10km/h relative to the truck in the direction of the truck's motion.What is the velocity of the ball relative to a stationary observer by the side of the road?What is the velocity of the ball relative to the driver of a car moving in the same direction as the truck at a speed of 80km/h ?
To find the velocity of the ball relative to a stationary observer by the side of the road, we need to consider the velocities of both the truck and the ball.
The velocity of the truck is given as 60 km/h. Since the truck is moving in a straight line and at a constant speed, this is also its velocity.
The ball has a velocity of 10 km/h relative to the truck, but we need to find its velocity relative to the stationary observer. To do this, we simply add the velocities of the truck and the ball together.
Velocity of the ball relative to the stationary observer = Velocity of the truck + Velocity of the ball
Therefore, Velocity of the ball relative to the stationary observer = 60 km/h + 10 km/h = 70 km/h
So, the velocity of the ball relative to a stationary observer by the side of the road is 70 km/h.
To find the velocity of the ball relative to the driver of a car moving in the same direction as the truck at a speed of 80 km/h, we again need to consider the velocities of the truck and the ball.
The velocities of the truck and the car are given as 60 km/h and 80 km/h, respectively. Since they are moving in the same direction, we can subtract the velocity of the truck from the velocity of the car to find the relative velocity between them.
Relative velocity of the car with respect to the truck = Velocity of the car - Velocity of the truck
Therefore, Relative velocity of the car with respect to the truck = 80 km/h - 60 km/h = 20 km/h
Now, we need to find the velocity of the ball relative to the driver of the car, which we can obtain by adding the relative velocity of the car with respect to the truck to the velocity of the ball relative to the truck.
Velocity of the ball relative to the driver of the car = Relative velocity of the car with respect to the truck + Velocity of the ball
Therefore, Velocity of the ball relative to the driver of the car = 20 km/h + 10 km/h = 30 km/h
So, the velocity of the ball relative to the driver of a car moving in the same direction as the truck at a speed of 80 km/h is 30 km/h.
To find the velocity of the ball relative to a stationary observer by the side of the road, we need to consider the velocities of the truck and the ball.
Step 1: Convert the velocities to meters per second for consistency.
- The velocity of the truck is 60 km/h. Converting to m/s: 60 km/h = (60 * 1000) / (60 * 60) = 16.67 m/s.
- The velocity of the ball relative to the truck is 10 km/h. Converting to m/s: 10 km/h = (10 * 1000) / (60 * 60) = 2.78 m/s.
Step 2: Add the two velocities to find the velocity of the ball relative to the stationary observer.
The velocity of the ball relative to the stationary observer is the sum of the velocities of the truck and the ball.
Velocity of the ball relative to the stationary observer = 16.67 m/s + 2.78 m/s = 19.45 m/s.
Therefore, the velocity of the ball relative to a stationary observer by the side of the road is 19.45 m/s.
Now, let's find the velocity of the ball relative to the driver of a car moving in the same direction as the truck at a speed of 80 km/h.
Step 1: Convert the velocities to meters per second for consistency.
- The velocity of the car is 80 km/h. Converting to m/s: 80 km/h = (80 * 1000) / (60 * 60) = 22.22 m/s.
Step 2: Subtract the velocity of the car from the velocity of the truck to find the relative velocity of the truck with respect to the car.
Relative velocity of the truck with respect to the car = 16.67 m/s - 22.22 m/s = -5.55 m/s.
(Note: The negative sign indicates that the truck is moving in the opposite direction to the car.)
Step 3: Add the relative velocity of the truck and the velocity of the ball relative to the truck to find the velocity of the ball relative to the driver of the car.
Velocity of the ball relative to the driver of the car = -5.55 m/s + 2.78 m/s = -2.77 m/s.
Therefore, the velocity of the ball relative to the driver of the car moving in the same direction as the truck at a speed of 80 km/h is -2.77 m/s (opposite to the direction of the car's motion).