The force shown in the figure below is the net eastward force acting on a ball. The force starts rising at t=0.020 s, falls back to zero at t=0.062 s, and reaches a maximum force of 55 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. Hint: Do not use J = FΔt. Look at the figure. Find the area of a nearly equally sized triangle.

I cannot make a good estimate without seeing the figure.

Use the pythagorean theorem

To determine the magnitude of the impulse delivered to the ball, we need to find the area under the force vs. time graph within the given time interval.

Since we have been given a hint to find the area of a nearly equally sized triangle, we can estimate the area under the graph by approximating the shape as a triangle.

Step 1: Calculate the base of the triangle
The base of the triangle can be determined by calculating the time difference between when the force starts to rise and falls back to zero. In this case, it is the time interval between t = 0.020 s and t = 0.062 s:

base = t_final - t_initial
base = 0.062 s - 0.020 s
base = 0.042 s

Step 2: Calculate the height of the triangle
The height of the triangle can be determined by finding the maximum force reached at the peak, which is given as 55 N.

height = maximum force
height = 55 N

Step 3: Calculate the area of the triangle
The area of a triangle can be calculated using the formula: area = (1/2) * base * height

area = (1/2) * base * height
area = (1/2) * 0.042 s * 55 N

Now, we can calculate the magnitude of the impulse delivered to the ball by finding the area under the graph within the given time interval:

impulse = area = (1/2) * 0.042 s * 55 N

Calculating this expression will give you the magnitude of the impulse delivered to the ball, with an error no bigger than 25% (high or low).