   SEARCH HOME Math Central Quandaries & Queries  Question from Jessi, a student: Ben is out at the practice range hitting golf balls. How much further will a golf ball with an initial speed of 75.0 m/s go when projected at 45.0 degree than when projected at 30.0 degree? Hi Jessi.

This is a question of projectile motion.

There are a couple of very important equations of projectile motion:

y = y0 + v0 t sinθ - ½ g t2.
x = x0 + v0 t cosθ.

Where y is the vertical location, x is the horizontal location, x0, y0 are the initial location, v0 is the initial velocity, t is the time since launch, θ is the angle between the initial trajectory and the ground and g is the constant acceleration due to gravity: 9.8 m/s2.

You can use the first equation for each value of θ to find t for each situation:
0 = 0 + 75 t sinθ - ½ g t2.

Once you have t for each angle, you can use it in the second equation, which describes the horizontal movement, to find where the ball strikes the ground.

I think you are meant to ignore special aerodynamic properties of golf balls, air resistance and how far it bounces!

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.