A boy in a car moving at 10 km/h [N] wants to throw a ball to a girl standing on the right-hand side of the road. He is able to throw the ball at 20 km/h. He wants the ball to go straight east, directly to her. a) Relative to the car which way should he throw in order to do this?
b) Relative to the ground, how fast will the ball travel to reach her?
I have this same question in Mr,Norisue's at Johnston Heights. I answer are:
a) [30 degrees S of E ]
b) 17km/hr
To answer both parts of the question, we need to consider the velocities of both the boy in the car and the ball relative to an observer on the ground.
Let's break down the problem step by step:
a) Relative to the car, the boy wants the ball to go straight east, directly to the girl standing on the right-hand side of the road. Since the car is moving north, the ball's velocity relative to the car should have a southward component to cancel out the car's northward velocity.
To visualize this, imagine two velocities vector arrows – one representing the car's velocity northwards and the other representing the ball's velocity southwards. These two velocity vectors should add up to zero when combined.
b) To determine the speed of the ball relative to the ground, we need to consider both the car's velocity and the ball's velocity. The ball's velocity relative to the ground will be the vector sum of the car's velocity and the ball's velocity relative to the car.
Given the car's velocity of 10 km/h to the north and the ball's velocity of 20 km/h relative to the car, the resulting velocity vector of the ball relative to the ground can be found using vector addition.
To perform the vector addition, we can break down the velocities into their respective components. The car's velocity consists entirely of a northward component, while the ball's velocity relative to the car has a southward component. Since we want the ball to go east, we can ignore the car's northward component.
By combining the car's northward velocity component and the ball's southward velocity component, we can find the resulting velocity vector of the ball relative to the ground. This resulting velocity will give us the speed at which the ball is traveling to reach the girl on the right-hand side of the road.
It's important to note that only the magnitudes (speeds) of the velocities are being added, as we are considering straight-line motion. The directions of the velocities are taken into account when determining their components and combining them.
By following these steps, you can determine both the relative direction in which the boy should throw the ball and the speed of the ball relative to the ground.