The force shown in the figure below is the net eastward force acting on a ball. The force starts rising at t=0.012 s, falls back to zero at t=0.062 s, and reaches a maximum force of 35 N at the peak. Determine with an error no bigger than 25% (high or low) the magnitude of the impulse (in N-s) delivered to the ball.

Area under the graph = impulse and is similar enough (less than 25% error) to be able to calculate the impulse of the curved graph.

A=(1/2)(b)(h)

A=(1/2)(0.062s-0.012s)(35N)

A=0.875N*s

To determine the magnitude of the impulse delivered to the ball, we need to find the area under the force-time graph. Since the force is varying with time, we can approximate the area by dividing it into two parts: the area of the rectangle and the area of the triangle.

1. Calculate the area of the rectangle:
- The height of the rectangle is the maximum force, which is 35 N.
- The base of the rectangle is the time duration when the force is constant, which is from t = 0.012 s to t = 0.062 s.
- Calculate the width (base) of the rectangle by subtracting the starting time from the ending time: base = 0.062 s - 0.012 s = 0.05 s.
- Calculate the area of the rectangle by multiplying the height (35 N) by the base (0.05 s).

2. Calculate the area of the triangle:
- The height of the triangle is the maximum force, which is 35 N.
- The base of the triangle is the width of the rectangle, which is 0.05 s.
- Calculate the area of the triangle by multiplying 0.5 by the height (35 N) by the base (0.05 s).

3. Add the areas of the rectangle and the triangle to get the total impulse delivered to the ball.

4. To find the error no bigger than 25%, we can calculate the maximum and minimum possible values for the impulse. To determine the maximum value, add the maximum possible error to the total impulse, and to determine the minimum value, subtract the maximum possible error from the total impulse.

By following this approach, you can calculate the magnitude of the impulse (in N-s) delivered to the ball and determine the maximum and minimum possible values considering the 25% error range.