A 143-g baseball is dropped from a tree 13.0 m above the ground.
With what speed would it hit the ground if air resistance could be ignored?
If it actually hits the ground with a speed of 8.00 m/s , what is the magnitude of the average force of air resistance exerted on it?
ignoring air resistance?
V^2=2gh
2nd part:
1/2 m vf^2+frictionforce*h=mgh
solve for frictionforce
To find the speed at which the baseball would hit the ground if air resistance is ignored, we can use the equation for free-fall motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and s is the distance.
In this case, the baseball is dropped from rest, so the initial velocity (u) is 0. The distance (s) is given as 13.0 m, and the acceleration due to gravity (a) is approximately 9.8 m/s^2.
Plugging these values into the equation, we have:
v^2 = 0^2 + 2 * 9.8 * 13.0
v^2 = 0 + 254.8
v^2 = 254.8
Taking the square root of both sides, we find:
v = √(254.8)
Calculating this value, we get:
v ≈ 15.98 m/s
Therefore, if air resistance is ignored, the baseball would hit the ground with a speed of approximately 15.98 m/s.
Now, to find the magnitude of the average force of air resistance exerted on the baseball, we can use the following equation:
F = (m * (v - u)) / t
where F is the force, m is the mass, v is the final velocity, u is the initial velocity, and t is the time taken.
In this case, the mass (m) of the baseball is given as 143 g, which is equivalent to 0.143 kg. The initial velocity (u) is 0 m/s, as the baseball is dropped from rest. The final velocity (v) is given as 8.00 m/s, and the time taken (t) is not given.
However, since we are asked to find the magnitude of the average force of air resistance, we can assume that the force is constant throughout. Therefore, the time taken (t) does not affect the calculation.
Plugging in the values, we have:
F = (0.143 * (8.00 - 0)) / t
F = (0.143 * 8.00) / t
F = 1.144 / t
Since the value of time is not provided, we cannot find the exact magnitude of the force of air resistance. Additionally, air resistance is a complex phenomenon that depends on various factors such as the shape and size of the object, the speed of the object, and the density of the air. To determine the exact magnitude of the average force of air resistance, you would need experimental data or complex calculations taking these factors into account.