Question

A bat hits a moving baseball. If the bat delivers a net eastward impulse of 1.5 N-s and the ball starts with an initial horizontal velocity of 3.8 m/s to the west and leaves with a 4.9 m/s velocity to the east, what is the mass of the ball (in grams)? (NEVER include units in the answer to a numerical question.)

Answer 1

To find the mass of the baseball, we can use the concept of impulse, which is equal to the change in momentum. We are given the net eastward impulse delivered by the bat and the initial and final velocities of the baseball. By using the equation for impulse, we can calculate the mass of the baseball to be 170 grams.

Step-by-step explanation:

To find the mass of the baseball, we can use the concept of impulse. Impulse is equal to the change in momentum, which is the product of mass and velocity. In this case, we are given the net eastward impulse delivered by the bat (1.5 N-s) and the initial and final velocities of the baseball (-3.8 m/s and 4.9 m/s, respectively).

Since the impulse is equal to the change in momentum, we can write the equation:

Impulse = (mass of the baseball)(final velocity - initial velocity)

Substituting the given values, we have:

1.5 = (mass of the baseball)(4.9 - (-3.8))

Simplifying the equation and solving for the mass of the baseball:

mass of the baseball = 1.5 / (4.9 - (-3.8))

mass of the baseball = 1.5 / 8.7

mass of the baseball = 0.17 kg

However, the question asks for the mass of the baseball in grams. Therefore, we need to convert the mass from kilograms to grams:

mass of the baseball = 0.17 kg * 1000 g/kg

mass of the baseball = 170 g

Answer 2

The mass of the ball is 5866 g.

Step-by-step explanation:

Given that,

Impulse = 1.5 N.s

Velocity to the west = 3.8 m/s

Velocity to the east = 4.9 m/s = -4.9 in to the west

We need to calculate the mass of the ball

Using formula of impulse

`I = p_(i)-P_(f)`

`I=m(v_(i)-v_(f))`

`m=(v_(i)-v_(f))/(I)`

Where,
`v_(i)` = initial velocity

`v_(f)` =final velocity

m = mass of ball

Put the value into the formula

`m=(3.9-(-4.9))/(1.5)`

`m=5.866\ kg`

`m = 5866\ g`

Hence, The mass of the ball is 5866 g.