Suppose a young child throws a tennis ball into the air as hard as he can. Which of the following is the most reasonable solution for the time it takes the ball to land?
A- (6 seconds)
B- (1.1 seconds)
C- (−2 seconds)
D- (10 seconds)
How high can a little kid throw it? Maybe thirty feet (10 meters) ?
potential energy at top = m g H
kinetic energy at throw = (1/2 ) m Vi^2
so 2 g H = Vi^2
H = Vi^2 / 2 g
g is about 10 m/s^2
H = Vi^2 / 20 = 10 meters
so Vi^2 = 200
Vi = about 14 m/s at the throw
v = Vi - g t = 14 - 10 t
at top v = 0 so about 1.4 seconds to get up to H
then 1.4 seconds to fall
so I think about 3 seconds
the issue is that is not one of the answer choices
ok nevermind it was 1.1
tiny kid :)
To determine the most reasonable solution for the time it takes the tennis ball to land, we can apply the laws of physics. The motion of the ball can be described using the equations of projectile motion. The two main factors affecting the time of flight are the initial velocity of the ball and the acceleration due to gravity.
When a ball is thrown vertically upward, it will experience a constant downward acceleration due to gravity. At the highest point of its trajectory, the vertical velocity of the ball becomes zero, and then it starts to fall back down. Therefore, the total time of flight is the sum of the time taken to reach the highest point and the time taken to come back down.
Based on this information, we can eliminate options C (−2 seconds) and D (10 seconds) as they do not align with the laws of physics. The time taken to reach the highest point should be less than the time taken to come back down.
Now, let's consider options A (6 seconds) and B (1.1 seconds).
Option A assumes the ball takes 6 seconds to return, but this time is too long for a tennis ball thrown vertically. It would suggest an extremely low initial velocity, which is unlikely if the child is throwing it as hard as they can. Therefore, we can confidently eliminate option A.
Option B suggests a time of 1.1 seconds, which seems more reasonable for a vertically thrown tennis ball. This option takes into account the initial velocity and the acceleration due to gravity, resulting in a shorter time of flight. Therefore, the most reasonable solution for the time it takes the ball to land is option B - 1.1 seconds.
In summary, the most reasonable solution is option B (1.1 seconds) based on the physics principles of projectile motion.