Question
Asked Nov 13, 2019
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A centerfielder fields a ground ball and attempts to make a 210​-ft throw to home plate. Given that the center fielder commonly makes long throws at 75 ​mph, find the two possible angles at which he can throw the ball to home plate. Find the time saved by choosing the smaller angle. I need a smaller and a larger angle.

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Expert Answer

Step 1

Here distance is 210 ft travelled by a projectile fired from the ground with an angle  and v0 = 75mph = 110ft/sec is the initial velocity.

 

The projectile motion is:

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sin 20 32d (110) sin 20 32 (210) 32(210) sin 20 (110) 6720 sin 20 12100 the angle 9 e (0,90) and the angle 20 E (0,180°) 672 20 sin = 33.74° 1210

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Step 2

So, possible value of 2  is 33.74 degree and 180 – 33.74 = 146.26  and possible value of  is 16.87 degree and 73.13 degree

 

Therefore, the possible angles are 16.87 degree and 73.13 degree.

 

Step 3

Part ( b) :

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(v, sin 0 ) Time of flight: 2t 2- for v16.86 110 - sin 1 6.87 = 6.5147 2t 2 9.8 for v-73.13 (110 sin 73.13 = 21.4829 2t 2 9.8

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