Relative Velocity of a pickup truck

[cbrons]

Homework Statement

A person riding in the back of a pickup truck traveling at 70 km/h on a straight, level road throws a ball with a speed of 15 km/h relative to the truck in the direction opposite to the truck's motion. What is the velociy of the ball (a) relative to a stationary observer by the side of the road, and (b) relative to the driver of car moving in the same direction as the truck at a speed of 90 km/h?

Homework Equations

VBT = 15 km/h
VBG = VBT + VTG
VBG = 15 km/h + 70 km/h

Trying to find the velocity of the ball with respect to the ground (observer)

I’m not sure if this is correct but the answer I got was 85 km/h

The Attempt at a Solution

My notes in class said add the velocity of the truck with respect to the ground plus the velocity of the ball with respect to the truck to get (a). I'm not sure where to start with (b)?

 

[Feldoh]

You don't really need any formula's to solve this. Just think about it logically for a second.

Before the ball is thrown in the direction opposite of the truck it is moving at the same speed as the truck right?

When the ball is thrown, if we pretend the truck is not moving, then the ball will look like it is traveling 15 km/h backwards by an observer in the truck.

But the truck is moving! So if the ball is 15 mph backwards from a truck moving 70 km/hr, two concidences logically follow.

1.) The ball has to be moving slower than the truck. This means that the ball cannot be moving 85 km/h, unfortunately.

2.) Relative to the stationary observer (the observer by the side of the road) the ball will be moving 70km/h - 15km/h

You must remember that velocity is a vector that has both a magnitude and direction, you accounted for the magnitude fine, but you switched the direction of the ball.

Does this make sense?

 

[baba89]

Your approach for finding the velocity of the ball with respect to the ground (observer) is correct. To find the velocity of the ball with respect to the driver of the car moving in the same direction as the truck, you can use the concept of relative velocity again. The velocity of the car with respect to the ground is 90 km/h, and the velocity of the truck with respect to the car is 70 km/h. Therefore, the velocity of the ball with respect to the car is the sum of these two velocities, which is 160 km/h. This means that the driver of the car will see the ball moving at a speed of 160 km/h in the same direction as the car.