A child pushes a 3.41 kilogram ball northward, in the water, with a force of 22.6 newtons. A current pushes the ball eastward with a force of 6.88 newtons. In what direction does the ball accelerate? ​Direction equals blank degrees. Fill in the blank.  Remember to indicate if the direction is positive, plus sign or negative, minus sign.

To determine the direction of acceleration, we analyze the forces acting on the ball as vectors and calculate the resultant direction.

### Step 1: Identify the forces and components
The two forces acting on the ball are:
- \( F_N = 22.6 \, \text{N} \) (northward)
- \( F_E = 6.88 \, \text{N} \) (eastward)

These forces form a right triangle, with \( F_N \) as the vertical component and \( F_E \) as the horizontal component.

### Step 2: Calculate the angle of acceleration
The direction \( \theta \) relative to the east axis can be found using the tangent function:
\[
\tan(\theta) = \frac{F_N}{F_E} = \frac{22.6}{6.88}
\]
Now, let's calculate \( \theta \):
The direction of acceleration is approximately \( +73.07 \) degrees relative to the east axis. This positive angle indicates that the acceleration is measured counterclockwise from the positive x-axis (eastward).

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### Related Questions
1. How would the direction change if the force of the current were stronger than the northward force?
2. What would be the resultant force acting on the ball in this scenario?
3. How do you determine acceleration if you know the resultant force and mass?
4. What happens if an additional force is introduced in the westward direction?
5. How does changing the mass of the ball affect the acceleration?

**Tip:** Always resolve forces into components when dealing with multi-dimensional problems.

A child pushes a 3.41 kilogram ball northward, in the water, with a force of 22.6 newtons. A current pushes the ball eastward with a force of 6.88 newtons. In what direction does the ball accelerate? Direction equals blank degrees.

Determine the direction of acceleration for a 3.41 kg ball pushed northward with a force of 22.6 N and eastward by a current with a force of 6.88 N. Learn how to apply vector addition, trigonometry, and Newton's Second Law to solve this physics problem.

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