A student throws two beanbags in the air, one straight
up and the other one at a 30° angle from the vertical.
Both beanbags are thrown with the same initial
velocity and from the same height. In your own
words, explain which one will come back and hit the
ground first and why.
The beanbag thrown straight up will come back and hit the ground first. This is because when an object is thrown straight up, it experiences a vertical acceleration due to gravity acting in the opposite direction. As it reaches the highest point of its trajectory, its velocity will gradually decrease to zero and then start falling back down.
On the other hand, the beanbag thrown at a 30° angle from the vertical will follow a curved path known as a projectile motion. This motion can be broken down into two components: horizontal and vertical. The horizontal component of the velocity remains constant throughout the motion, while the vertical component is affected by gravity.
Since both beanbags are thrown with the same initial velocity and from the same height, the vertical velocity component will be the same for both. However, the beanbag thrown at an angle will have an additional horizontal velocity component.
Due to the curved path, the beanbag thrown at a 30° angle will take a longer time to reach its highest point compared to the one thrown straight up. Therefore, it will take more time for it to start falling back down and ultimately hit the ground. As a result, the beanbag thrown straight up will hit the ground first.
Well, let me juggle with some knowledge here. Alright, so we have two beanbags being thrown by a student. One goes straight up, and the other one is a bit of a daredevil at a 30° angle. Now, if we consider that both beanbags were thrown with the same initial velocity and from the same height, the one that will hit the ground first will be the straight-up beanbag.
Why, you ask? Well, it's all about the angle of attack! The vertically-thrown beanbag only needs to overcome the gravitational force pulling it downward, while the angled beanbag needs to fight gravity AND travel a longer distance horizontally. So, while Mr. Straight-up is busy taking the shortcut back to Earth, Mr. Daredevil Angle has to take a bit of a detour before saying hello to the ground.
To determine which beanbag will hit the ground first, we need to consider the motion of the two beanbags separately.
Let's start with the beanbag thrown straight up. When an object is thrown vertically upwards, the only force acting on it is gravity pulling it downwards. As the beanbag goes higher, its velocity decreases until it reaches the maximum height. Then, gravity starts to pull it back down, and the beanbag accelerates downwards due to gravity. Eventually, it reaches the ground.
Now let's consider the beanbag thrown at a 30° angle from the vertical. This beanbag has both horizontal and vertical components of motion. The vertical component follows a similar path as the beanbag thrown straight up, while the horizontal component moves the beanbag in a curved path. This curved path doesn't affect the time it takes for the beanbag to come back down to the ground.
Now, since both beanbags were thrown with the same initial velocity and from the same height, the initial vertical velocity is the same for both beanbags. Therefore, the time it takes for both beanbags to reach the same maximum height will be the same.
However, the beanbag thrown straight up only has to overcome gravity to come back down, whereas the beanbag thrown at an angle needs to overcome gravity and also cover horizontal distance. So, the beanbag thrown straight up will hit the ground first.
In summary, the beanbag thrown straight up will hit the ground first because it only needs to overcome gravity, while the beanbag thrown at an angle needs to cover both horizontal and vertical distances.
The beanbag that was thrown at 30o will
return and hit ground first, because its' vertical component of initial velocity is less than that of the bag that was thrown straight up. Yo = Vo*cos30. So it is less by a factor of 0.866.