A baseball pitcher throws the ball towards the batter at 90 mph. His bat connects with the ball for a line drive, after which the ball is moving back towards the pitcher at 110 …

Question

asked Dec 26, 2020 76.3k views

1 Answer

Sziraqui · Answer 1 · 2020-12-30T17:25:36+0000

Answer:

F=-18412.9N , where the minus indicates the direction is opposite to that of the throw.

Step-by-step explanation:

a)

Since MKS stands for meter-kilogram-second and we know that:

$1\ hour = 3600\ seconds$

$1\ mile = 1600\ meters$

1000g = 1kg

We can write that:

$(1\ hour)/(3600\ seconds)=1$

$(1600\ meters)/(1\ mile)=1$

(1kg)/(1000g)=1

These are conversion factors, equal to 1, so multiplying our results by them won't change their value, only their units.

So we have that:

$90 mph=90 (miles)/(hour)((1\ hour)/(3600\ seconds))((1600\ meters)/(1\ mile))=40m/s$

$110 mph=110 (miles)/(hour)((1\ hour)/(3600\ seconds))((1600\ meters)/(1\ mile))=48.89m/s$

145 g=145 g((1kg)/(1000g))=0.145kg

b)

Newton's 2nd Law tells us that F=ma, and the definition of acceleration is
$a=(\Delta v)/(\Delta t)$ , so we have:

$F=m(\Delta v)/(\Delta t)=m(v_f-v_i)/(t)$

Taking the throw direction as the positive one, for our values we have:

F=m(v_f-v_i)/(t)=(0.145kg)((-48.89m/s)-(+40m/s))/(0.0007s)=-18412.9N