A ball is thrown upwards. What is its initial vertical speed? The acceleration
of gravity is 9.8 m/s^2
and maximum
height is 4.6 m ,. Neglect air resistance.
Answer in units of m/s
To find the initial vertical speed of the ball thrown upwards, we can use the equation of motion for vertical motion:
v^2 = u^2 - 2as
where:
v is the final vertical velocity (0 m/s when the ball reaches its maximum height and starts falling down)
u is the initial vertical velocity (which we need to find)
a is the acceleration due to gravity (-9.8 m/s^2, negative because it is acting against the motion of the ball upwards)
s is the displacement (maximum height = 4.6 m)
Plugging in the given values, we have:
0 = u^2 - 2(-9.8)(4.6)
Simplifying,
0 = u^2 + 2(9.8)(4.6)
0 = u^2 + 2(44.98)
0 = u^2 + 89.96
Let's solve for u:
u^2 = -89.96
u = ±√(-89.96)
Since velocity cannot be negative in this case (as it is being thrown upwards), the initial vertical speed is:
u ≈ √(89.96)
u ≈ 9.49 m/s
Therefore, the initial vertical speed of the ball thrown upwards is approximately 9.49 m/s.
To find the initial vertical speed of the ball when it is thrown upwards, we can use the kinematic equation:
vf = vi + at
Where:
- vf is the final velocity of the ball
- vi is the initial velocity of the ball
- a is the acceleration of gravity
- t is the time
At the maximum height, the ball's final velocity is 0 because it momentarily stops before falling back down.
Since the ball is thrown upwards, we can assume the vertical speed will have a negative sign. This is because the acceleration due to gravity acts in the downward direction.
Using the given information, let's find the time it takes for the ball to reach the maximum height:
We can use the kinematic equation:
vf^2 = vi^2 + 2ad
Where:
- d is the displacement or height
- a is the acceleration of gravity
Rearranging the equation, we get:
vi = sqrt(vf^2 - 2ad)
Substituting the given values:
vf = 0 m/s (at maximum height)
d = 4.6 m
a = 9.8 m/s^2
vi = sqrt(0^2 - 2 * 9.8 * 4.6)
vi = sqrt(0 - 90.16)
vi = sqrt(-90.16)
Since the answer is in units of m/s, taking the square root of a negative number is not possible. This indicates that there was an error in the calculations or the given information. Please check the values provided and try again.
V^2 = Vo^2 + 2g*h.
V = 0.
g = -9.8 m/s^2.
h = 4.6 m., max.
Vo = ?.