The hammer throw is a track-and-field event, popular in Scotland, in which a ball on a rope (the "hammer") is whirled around the thrower in a circle before being released. The goal is the send the ball as a projectile as far down the field as possible. At a track meet, the circle in which a ball is whirled by a hammer thrower is at a 45° angle to the ground. To achieve the longest distance, at what point in its tilted circular orbit should the thrower release the ball?
a. at it's lowest point
b. at it's highest point
c. halfway as it moves from it's lowest point to it's highest point
d. halfway as it moves from it's highest point to it's lowest point
c, of course.
Thanks
To determine at which point in the tilted circular orbit the thrower should release the ball to achieve the longest distance, we need to consider the principles of projectile motion.
When a projectile is launched at an angle to the ground, it follows a curved path known as a parabola. The range of the projectile (i.e., the distance it travels) is maximized when it is released at an angle of 45° to the horizontal.
In the case of the hammer throw, the thrower is spinning and releasing the ball within a tilted circular orbit. However, the key principle remains the same: releasing the ball at a 45° angle to the horizontal will result in the longest distance.
Now, let's analyze the given choices:
a. Releasing the ball at its lowest point (when it is closest to the ground) would result in a trajectory with a smaller angle to the horizontal. This would lead to a shorter range and therefore is not the optimal point of release.
b. Releasing the ball at its highest point (when it is furthest from the ground) would also result in a trajectory with a smaller angle to the horizontal. Similar to choice a, this would result in a shorter range and is not the optimal point of release.
c. Releasing the ball halfway as it moves from its lowest point to its highest point would have the ball traveling at an upward angle. This would lead to a shorter range compared to releasing it at a 45° angle.
d. Releasing the ball halfway as it moves from its highest point to its lowest point would have the ball traveling at a downward angle. Similar to choice c, this would result in a shorter range compared to releasing it at a 45° angle.
Therefore, the optimal point in the tilted circular orbit for the thrower to release the ball is:
**b. at its highest point**
By releasing the ball at its highest point in the tilted circular orbit, where it is furthest from the ground, the thrower can achieve a trajectory with a 45° angle to the horizontal and maximize the range of the throw.