Question

Two golfers each hit a ball at the same speed, but one at 60 degrees with the horizontal and the other 30 degrees. a. Which ball goes farther? b. Which hits the ground first?

Answer 1

Answer:

Therefore, both balls will hit the ground at the same distance from their respective starting points and at the same time.

Explanation:

Both balls will hit the ground at the same distance and at the same time assuming they both start at the same initial elevation from the ground.

We know that range in the projectile motion given as

$R=\dfrac{v_o^2sin2\theta}{g}$

sin 60° = sin 120° =0.866

Therefore, the maximum range will be identical assuming both golfers hit the ball at the same elevation from the ground.

As for the time...

Where v is 0 m/s (final velocity at highest point), v0 is the initial velocity (for both golfers) and is the acceleration due to gravity (-9.8 m/s^²). As you can see, the time it takes to get to the highest point is independent of the angle; it is only dependent on the initial velocity. Since both golfers hit the ball with the same speed, the time for the ball to reach the highest point will be the same. Also, since it's a parabola, you can multiply the time by 2 for each golfer to get the time it takes to hit the ground.

Therefore, both balls will hit the ground at the same distance from their respective starting points and at the same time.