I. Vector Calculus (10 points each except where indicated for a total of 70 Poin

Question

I. Vector Calculus (10 points each except where indicated for a total of 70 Points) All works should shown and written on the test. Decimals are unaccepted as answers except where indicated Be mindful of significant figures and units. 1. Flight of a golf ball. A golf ball is driven down a horizontal fairway with an initial speed of ss m at an initial angle of 250 (from a tee with negligible height). Neglect all forces except gravity assume that the ball's trajectory lies in a plane. a.) How far does the ball travel horizontally and when does it land? b.) What is the maximum height of the ball? c.) At what angles should the ball be hit to reach a green that is 300.0 m from the tee?

Explanation / Answer

Sol:

First, determine the horizontal and vertical components of the initial velocity

vx = vi cosq = (55m/ s)(cos25) = 49.8469m/ s

viy = vi sinq = (55m/ s)(sin25) =23.244m/ s

Need to determine the time it took to land:

y = viy t + 1/ 2 at2

0m = (23.24m/ s)t + 1/ 2 (-9.81m/ s2 )t 2

t=0 or

t=4.74 s

x = vxt =  49.8469m/ s * 4.74 = 236.27 m

The range of the ball is 236.27 meters

b)

Half the flight time will be 2.37 seconds.

y = viy t + 1 /2 at2

= 23.244 *2.37 + 1/2 (-9.8) ( 2.37)^2

= 27.565 m

The ball will reach a maximum height of 27.565 meters

c)

assuming the same 55 m/s initial speed,
find t when x=300
use that t to find v in

vt-16t^2 = 300 => 4.74 (v - 16 * 4.74) = 300 => v= 139

then sin = v/55 = 139 /55 => = sin-1 (139/55)

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