A boat is traveling upstream in the positive direction of an x axis at 14 km/h with respect to the water of a river. The water is flowing at 9.0 km/h with respect to the ground (parallel to the boat). What are the (a) magnitude and (b) direction of the boat’s velocity with respect to the ground? A child on the boat walks from front to rear at 6.0 km/h with respect to the boat. What are the (c) magnitude and (d) direction of the child’s velocity with respect to the ground?

Are you and hanrap the same person? These are vector addition problems.

We will be glad to critique your work

omg this is soooooooooooooo hard

To solve this problem, we can use vector addition and subtraction. Let's break it down step by step:

(a) Magnitude of the boat's velocity with respect to the ground:

To find the magnitude of the boat's velocity with respect to the ground, we need to subtract the velocity of the water from the velocity of the boat.

Magnitude of the boat's velocity with respect to the ground = Magnitude of the boat's velocity - Magnitude of the water's velocity

Magnitude of the boat's velocity = 14 km/h
Magnitude of the water's velocity = 9.0 km/h

Therefore, magnitude of the boat's velocity with respect to the ground = 14 km/h - 9.0 km/h = 5.0 km/h.

(b) Direction of the boat's velocity with respect to the ground:

The boat is traveling upstream, which means it is moving in the positive direction of the x-axis. The water is flowing parallel to the boat, so the direction of the boat's velocity with respect to the ground will be the same as its direction with respect to the x-axis. Thus, the direction of the boat's velocity with respect to the ground is positive.

(c) Magnitude of the child's velocity with respect to the ground:

The child is walking from front to rear of the boat, which means the child's velocity is in the same direction as the boat's velocity. Therefore, the magnitude of the child's velocity with respect to the ground will be the same as the magnitude of the boat's velocity, which is 14 km/h.

(d) Direction of the child's velocity with respect to the ground:

Since the child's velocity is in the same direction as the boat's velocity, the direction of the child's velocity with respect to the ground will be the same as the direction of the boat's velocity, which is positive.

To solve this problem, we need to analyze the velocities of the boat and the child with respect to the ground.

Let's break down the given information:

Boat's velocity with respect to the water (Vbw): 14 km/h in the positive direction of the x-axis.
Water's velocity with respect to the ground (Vwg): 9.0 km/h in the positive direction parallel to the boat.
Child's velocity with respect to the boat (Vcb): 6.0 km/h from front to rear.

(a) To find the magnitude of the boat's velocity with respect to the ground (Vbg), you can simply add the velocities of the boat and the water. So we have:
Vbg = Vbw + Vwg = 14 km/h + 9.0 km/h = 23 km/h.

(b) The direction of the boat's velocity with respect to the ground will always be in the positive x-direction because the water flow is parallel to the boat. Therefore, the direction of Vbg is in the positive direction of the x-axis.

(c) To find the magnitude of the child's velocity with respect to the ground (Vcg), we need to consider the relative motion of the child with respect to the ground.
Since the child is on the boat, the child's velocity with respect to the ground (Vcg) will be the vector sum of the boat's velocity with respect to the ground (Vbg) and the child's velocity with respect to the boat (Vcb). So we have:
Vcg = Vbg + Vcb = 23 km/h + 6.0 km/h = 29 km/h.

(d) The direction of the child's velocity with respect to the ground will also be in the positive x-direction, as the child is moving in the same direction as the boat.

Therefore, the answers are:
(a) The magnitude of the boat's velocity with respect to the ground is 23 km/h.
(b) The direction of the boat's velocity with respect to the ground is in the positive direction of the x-axis.
(c) The magnitude of the child's velocity with respect to the ground is 29 km/h.
(d) The direction of the child's velocity with respect to the ground is in the positive direction of the x-axis.