A ball moving at a speed of 2.0 m/s rolls off a horizontal table. If the table is 1.2 m high, how far does the ball travel horizontally in m when it strikes the floor
To find the horizontal distance traveled by the ball when it strikes the floor, we need to determine the time it takes for the ball to fall from the table and then use that time to calculate the horizontal distance.
First, let's find the time it takes for the ball to fall from a height of 1.2 m using the equation for free fall:
h = (1/2) * g * t^2,
where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Rearranging the equation for time, we have:
t = sqrt(2h / g).
Substituting the given values, we get:
t = sqrt(2 * 1.2 / 9.8) = sqrt(0.2449) ≈ 0.49 s.
Now that we know the time, we can find the horizontal distance traveled by the ball using the equation:
d = v * t,
where v is the initial horizontal velocity of the ball and t is the time.
Given that the ball is moving at a speed of 2.0 m/s, the horizontal distance becomes:
d = 2.0 m/s * 0.49 s = 0.98 m.
Therefore, when the ball strikes the floor, it travels approximately 0.98 m horizontally.
To find the horizontal distance traveled by the ball when it strikes the floor, we can use the formula for horizontal distance covered in free fall:
d = v * t
where:
d = horizontal distance
v = horizontal velocity
t = time of fall
First, we need to calculate the time of fall. Since the ball is rolling off a horizontal table, its initial vertical velocity is zero, and it is subject only to the acceleration due to gravity (-9.8 m/s²). We can use the kinematic equation to find the time of fall:
h = (1/2) * g * t²
where:
h = height (1.2 m)
g = acceleration due to gravity (-9.8 m/s²)
t = time of fall
Rearranging the equation to solve for t:
t² = (2 * h) / g
t² = (2 * 1.2) / 9.8
t² = 0.2449
t = √0.2449
t ≈ 0.4949 s
Now, we can calculate the horizontal distance using the formula:
d = v * t
d = 2.0 * 0.4949
d ≈ 0.9898 m
Therefore, the ball travels approximately 0.9898 meters horizontally when it strikes the floor.
How far away did the ball land from the table?
t=D/S
t= 1.2m÷2m/s
t= 0.6 s
D=1/2 at^2
D=0.5*(9.8 m/s/s) * 0.6^2
D= 4.9 m/s/s * 0.36
D= 1.764m
rounded to sig. figures: 1.8 m