In a good hit, a baseball and bat are in contact with each other for about 1 millisecond. In the first game of the 2012 World Series, Tigers pitcher Justin Verlander threw a 90-mph pitch to the Giants’ Pablo Sandoval. Sandoval’s hit returned the ball directly back at Verlander at 70 mph. Calculate the average force of the bat on the ball, during the contact. Round the final answer to the nearest whole number.

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11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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In a good hit, a baseball and bat are in contact with each other for about 1 millisecond. In the first game of the 2012 World Series, Tigers pitcher Justin Verlander threw a 90-mph pitch to the Giants’ Pablo Sandoval. Sandoval’s hit returned the ball directly back at Verlander at 70 mph. Calculate the average force of the bat on the ball, during the contact. Round the final answer to the nearest whole number.

The size and mass of common balls are listed, together with typical values of speed and spin relevant to play.
Radius
Mass
Ball
Spin
cm
ft
kg
slug
m/s
mph
rps
2
6.56 x 10-2
2.7x 10-3
1.86x 10-4
Table tennis
9-25
20-55
10-25
2.13
6.99 x 10-2
0.045
3.10x 10-3
Golf
Up to 65 Up to 145 Up to 180!
3.18
1.04 x 10-1
0.057
3.93 x 10-3
Tennis ball
30
65
30
3.2
1.05 x 10-1
0.145
1.00x 10-2
Lacrosse ball
30-50
65-110
?
3.74
1.23 x 10-1
0.15
1.03 x 10-2
Baseball
25-45
55–100
up to 20
2.86
9.38 x 10-2
0.156
1.08 x 10-2
Numbered billiard ball
2.86
9.38 x 10-2
0.17
1.17× 10-2
Billiard cue ball (heavy)
0.5-8
1–15
3.58
1.17x 10-1
0.16
1.10x 10-2
Cricket
10
-
-
3.81
1.25 x 10-1
0.17
1.17× 10-2
Hockey puck (h= 2.54 cm)
20-43
45-95
4.85
1.59 x 10-1
0.185
1.28 x 10-2
Softball
18-32
40–70
?
10.5
3.44 x 10-1
0.27
1.86x 10-2 | Volleyball
15-25
35-55
3-6 (est.)
8.9
2.92 x 10-1
0.42
2.90x 10-2
Football (1 = 28 cm)
18-26
40-60
10 (spiral)
11.1
3.64x 10-1
0.425
2.93 x 10-2
Soccer ball
15-25
35-55
10
10.5
3.44 x 10-1
0.425
2.93 x 10-2
Women's water polo
11.1
3.64 x 10-1
0.425
2.93 x 10-2
Men's water polo
11.6
3.80 x 10-1
0.54
3.72x 10-2
Women's basketball (size 6)
5-10
10-25
2
12
3.94 x 10-1
0.62
4.28 x 10-2
Men's basketball (size 7)
5–10
10-25
2
18
5.90 x 10-1
1
6.90x 10-2
Women's discus
15-25
34-56
22
7.22 x 10-!
2
1.38× 10-!
Men's discus
15-25
34-56
1.64 x 10-1
4
2.76x 10-1
Women's 4-kg shot
10–14
22–32
6.
1.97× 10-1
7.26
5.01x 10-1
Men's 16-lb shot
10–14
22–32
10.9
3.58 x 10-1
7.26
5.01x 10-1
Bowling ball, 16 lb
6-10
15-25
7.3
5.03 x 10-1
Carbon bike
8-20
18-45
14
4.59 x 10-1
18.2
1.26
Curling stone
3
7
Transcribed Image Text:The size and mass of common balls are listed, together with typical values of speed and spin relevant to play. Radius Mass Ball Spin cm ft kg slug m/s mph rps 2 6.56 x 10-2 2.7x 10-3 1.86x 10-4 Table tennis 9-25 20-55 10-25 2.13 6.99 x 10-2 0.045 3.10x 10-3 Golf Up to 65 Up to 145 Up to 180! 3.18 1.04 x 10-1 0.057 3.93 x 10-3 Tennis ball 30 65 30 3.2 1.05 x 10-1 0.145 1.00x 10-2 Lacrosse ball 30-50 65-110 ? 3.74 1.23 x 10-1 0.15 1.03 x 10-2 Baseball 25-45 55–100 up to 20 2.86 9.38 x 10-2 0.156 1.08 x 10-2 Numbered billiard ball 2.86 9.38 x 10-2 0.17 1.17× 10-2 Billiard cue ball (heavy) 0.5-8 1–15 3.58 1.17x 10-1 0.16 1.10x 10-2 Cricket 10 - - 3.81 1.25 x 10-1 0.17 1.17× 10-2 Hockey puck (h= 2.54 cm) 20-43 45-95 4.85 1.59 x 10-1 0.185 1.28 x 10-2 Softball 18-32 40–70 ? 10.5 3.44 x 10-1 0.27 1.86x 10-2 | Volleyball 15-25 35-55 3-6 (est.) 8.9 2.92 x 10-1 0.42 2.90x 10-2 Football (1 = 28 cm) 18-26 40-60 10 (spiral) 11.1 3.64x 10-1 0.425 2.93 x 10-2 Soccer ball 15-25 35-55 10 10.5 3.44 x 10-1 0.425 2.93 x 10-2 Women's water polo 11.1 3.64 x 10-1 0.425 2.93 x 10-2 Men's water polo 11.6 3.80 x 10-1 0.54 3.72x 10-2 Women's basketball (size 6) 5-10 10-25 2 12 3.94 x 10-1 0.62 4.28 x 10-2 Men's basketball (size 7) 5–10 10-25 2 18 5.90 x 10-1 1 6.90x 10-2 Women's discus 15-25 34-56 22 7.22 x 10-! 2 1.38× 10-! Men's discus 15-25 34-56 1.64 x 10-1 4 2.76x 10-1 Women's 4-kg shot 10–14 22–32 6. 1.97× 10-1 7.26 5.01x 10-1 Men's 16-lb shot 10–14 22–32 10.9 3.58 x 10-1 7.26 5.01x 10-1 Bowling ball, 16 lb 6-10 15-25 7.3 5.03 x 10-1 Carbon bike 8-20 18-45 14 4.59 x 10-1 18.2 1.26 Curling stone 3 7
Expert Solution
Step 1: Given data

Solution:

Given that:

vi = 90 mph = 40.2336 m/s

vf = -70 mph = -31.2928 m/s

Δt = 1 millisecond =1x10-3 s

Note: Velocity has direction, After the hit, ball travels in opposite direction. 



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