A 3.79 kg ball is dropped from the roof of
a building 163.8 m high. While the ball is
falling to Earth, a horizontal wind exerts a
constant force of 11.5 N on the ball. It takes 5.77 second to hit the ground.
How far from the building does the ball hit
the ground?
Answer in units of m.
The horizontal wind will not affect the time it takes to fall. Get that time (T) from the equation
(1/2) gT^2 = 163.8 m
Whoops, they already told you the time to fall, 5.77 s. It agrees with the above equation.
The sideways acceleration of the ball is
a_x = F/m = 3.03 m/s^2
The horizontal displacement at the ground is
X = (1/2)*a_x*T^2
To find the distance from the building where the ball hits the ground, we need to calculate the horizontal distance traveled by the ball.
The horizontal distance traveled by the ball can be found using the formula:
distance = velocity * time
To find the horizontal velocity of the ball, we need to determine the net horizontal force acting on the ball.
The only horizontal force acting on the ball is the wind force, which is constant at 11.5 N. This force causes an acceleration in the horizontal direction:
F = m * a
11.5 N = 3.79 kg * a
Solving for the acceleration:
a = 11.5 N / 3.79 kg
a ≈ 3.034 m/s^2
Using this acceleration, we can find the horizontal velocity (v) of the ball after 5.77 seconds:
v = a * t
v = 3.034 m/s^2 * 5.77 s
v ≈ 17.517 m/s
Now that we have the horizontal velocity, we can calculate the distance using the formula mentioned earlier:
distance = velocity * time
distance = 17.517 m/s * 5.77 s
distance ≈ 101.0619 m
Therefore, the ball hits the ground approximately 101.0619 meters away from the building.
To find the distance from the building where the ball hits the ground, we can use the equations of motion.
First, let's find the time it takes for the ball to fall to the ground. We know that the acceleration due to gravity is approximately 9.8 m/s² and the initial velocity is 0 m/s:
Using the equation of motion:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time²
We can rearrange the equation to solve for time:
0.5 * Acceleration * Time² = Distance
Substituting the values:
0.5 * (9.8 m/s²) * (5.77 s)² = Distance
Simplifying the equation:
Distance = 0.5 * (9.8 m/s²) * (33.3129 s²)
Distance = 162.870 m
Therefore, the ball hits the ground approximately 162.870 meters away from the building.