A 2.98 kg ball is dropped from the roof of a building 158.3 m high. While the ball is falling to Earth, a horizontal wind exerts a constant force of 13.1 N on the ball.
A.)How long does it take to hit the ground? The acceleration of gravity is 9.81 m/s^2. Answer in units of s
B.)How far from the building does the ball hit the ground? Answer in units of m
C.)What is its speed when it hits the ground? Answer in units of m/s
To solve these problems, we can use the equations of motion and the principles of physics.
A.) To find the time it takes for the ball to hit the ground, we can use the equation of motion:
\[s = ut + \frac{1}{2}at^2\]
where:
s = distance (158.3 m)
u = initial velocity (0 m/s, since the ball is dropped)
a = acceleration (acceleration due to gravity, -9.81 m/s^2)
t = time
Rearranging the equation, we get:
\[t = \sqrt{\frac{2s}{a}}\]
Plugging in the given values, we have:
\[t = \sqrt{\frac{2 \times 158.3}{9.81}}\]
Evaluating this expression will give us the time it takes for the ball to hit the ground.
B.) To find how far from the building the ball hits the ground, we need to calculate the horizontal distance. Since there is no horizontal force acting on the ball, it will continue to move horizontally with a constant velocity.
We can use the equation:
\[d = vt\]
where:
d = distance (what we are trying to find)
v = horizontal velocity (which remains constant throughout the motion)
t = time (which we found in part A)
Since the wind exerts a constant force of 13.1 N on the ball, we can find the horizontal acceleration using Newton's second law:
\[F = ma\]
\[a = \frac{F}{m}\]
where:
F = force applied by the wind (13.1 N)
m = mass of the ball (2.98 kg)
Once we have the horizontal acceleration, we can calculate the horizontal velocity by multiplying it by the time we found in part A. Then, we can use this velocity to calculate the horizontal distance the ball travels.
C.) To find the speed of the ball when it hits the ground, we can use the equation:
\[v = u + at\]
where:
v = final velocity (what we are trying to find)
u = initial velocity (which is 0 m/s)
a = acceleration due to gravity (-9.81 m/s^2)
t = time (which we found in part A)
Evaluating this expression will give us the speed of the ball when it hits the ground.