A baseball (m = 145 g) traveling 20 m/s moves a fielder's glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

Magnitude
N
Direction
in the direction opposite to the ball's motion
in the direction of the ball's motion
perpendicular to the ball's motion

To find the average force exerted by the ball on the glove, we can use Newton's second law of motion, which states that the force on an object is equal to the mass of the object multiplied by its acceleration:

Force = mass * acceleration

In this case, the mass of the ball is given as 145 grams, which we need to convert to kilograms (1 kg = 1000 g). Thus,

Mass of the ball = 145 g ÷ 1000 g/kg = 0.145 kg

The acceleration of the ball can be found using the equation for average acceleration:

Acceleration = (change in velocity) / (time taken)

Since the ball is caught and brought to rest, its final velocity is 0 m/s. Therefore, the change in velocity is:

Change in velocity = final velocity - initial velocity = 0 m/s - 20 m/s = -20 m/s

The change in velocity is negative because the ball is slowing down in the direction opposite to its motion.

The distance the glove moves backward when catching the ball is given as 25 cm. We also need to convert this to meters:

Distance = 25 cm ÷ 100 cm/m = 0.25 m

Now, let's calculate the time taken:

Distance = (initial velocity * time) + (0.5 * acceleration * time^2)

0.25 m = (20 m/s * time) + (0.5 * -20 m/s^2 * time^2)

This is a quadratic equation that we can solve to find the time taken. However, since the question only asks for the average force, we don't need to find the exact time. We can assume that the time taken is small enough so that the acceleration is approximately constant.

Next, let's calculate the acceleration using the above equation:

0.25 m = (20 m/s * time) + (0.5 * -20 m/s^2 * time^2)

Simplifying this equation, we get:

0.25 m = 20 m/s * time - 10 m/s^2 * time^2

Now, we can differentiate both sides of the equation with respect to time to find the acceleration:

0 = 20 m/s - 20 m/s^2 * time

Simplifying this equation, we get:

time = 1 s

Now that we have the time taken, we can calculate the acceleration:

Acceleration = (change in velocity) / (time taken) = -20 m/s / 1 s = -20 m/s^2

The negative sign indicates that the acceleration is in the opposite direction of the ball's motion.

Finally, we can calculate the force using Newton's second law:

Force = mass * acceleration = 0.145 kg * -20 m/s^2 = -2.9 N

Since the force is negative, it means it is in the direction opposite to the ball's motion. Therefore, the average force exerted by the ball on the glove is 2.9 N in the direction opposite to the ball's motion.