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<u>Answer:</u>
a) Time spend by ball in air = 4.368 seconds
b) Longest hole that golfer can make = 93.59 meter
<u>Explanation:</u>
Projectile motion has two types of motion Horizontal and Vertical motion.
Vertical motion:
We have equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.
Considering upward vertical motion of projectile.
In this case, Initial velocity = vertical component of velocity = u sin θ, acceleration = acceleration due to gravity = -g and final velocity = 0 m/s.
0 = u sin θ - gt
t = u sin θ/g
Total time for vertical motion is two times time taken for upward vertical motion of projectile.
So total travel time of projectile = 2u sin θ/g
Horizontal motion:
We have equation of motion , , s is the displacement, u is the initial velocity, a is the acceleration and t is the time.
In this case Initial velocity = horizontal component of velocity = u cos θ, acceleration = 0 and time taken = 2u sin θ /g
So range of projectile,
a) We have golf ball travels maximum distance, so range is maximum.
Maximum range is when, sin 2θ =1
=> θ = 45⁰
Now we have travel time of projectile, t = 2u sin θ/g
Initial velocity = 30.3 m/s and θ = 45⁰
So time spend in air, t =
b) Longest hole that golfer can make = Range of projectile =
Longest hole that golfer can make =