A ball is thrown vertically upwards from the ground and it reaches a height of 20m. Calculate
the speed the ball had when it was launched.
I don't know how to solve this due to the fact that in the problem we only have the height as data , not even mass.
the kinetic energy of the ball at launch equals the gravitational potential energy at the peak
½ m v² = m g h
v = √(2 g h) = √(2 * 9.8 * 20) m/s
But wait oh did you get the mass?
To find the initial speed (also known as the launch speed) of the ball, we can use the kinematic equation for vertical motion. In this scenario, the ball is thrown vertically upwards, so the only force acting on it is gravity.
The kinematic equation that relates the initial velocity, final velocity, acceleration, and displacement is:
𝑣² = 𝑢² + 2𝑔ℎ
where
𝑣 is the final velocity (which is zero when the ball reaches its maximum height),
𝑢 is the initial velocity (what we want to find),
𝑔 is the acceleration due to gravity (approximately 9.8 m/s²), and
ℎ is the vertical displacement (which is 20 m in this case).
Substituting the known values into the equation:
0 = 𝑢² + 2(9.8)(20)
Simplifying the equation:
0 = 𝑢² + 196
Rearranging the equation to solve for 𝑢:
𝑢² = -196
Taking the square root of both sides:
𝑢 = ±√(-196)
Since speed cannot be negative, we discard the negative solution.
Therefore, the speed or initial velocity of the ball when it was launched (in the upward direction) is the square root of 196, which is approximately 14 m/s.
Please note that we assumed no air resistance and that the ball experiences free fall.