Question

a golf ball is hit with a velocity of 30.0 m/s at an angle of 25 degrees about the horizontal. how long is the ball in the air and does the ball make it to the green which is 60.0 m away

Answer 1

Ok so use trigonometry to work out the vertical component of velocity.

sin(25) =opp/hyp
rearrange to:
30*sin(25) which equals 12.67ms^-1

now use SUVAT to get the time of flight from the vertical component,

V=U+at

Where V is velocity, U is the initial velocity, a is acceleration due to gravity or g. and t is the time.

rearranges to t= (V+u)/a

plug in some numbers and do some maths and we get 2.583s

this is the total air time of the golf ball.

now we can use Pythagoras to get the horizontal component of velocity.

30^2-12.67^2= 739.29
sqrt739.29 = 27.19ms^-1

and finally speed = distance/time

so--- 27.19ms^-1*2.583s= 70.24m

The ball makes it to the green, and the air time is 2.58s