Nicole throws a ball straight up.Chad watches the ball from a window 5meters above the point where Nicole released it . The ball passes Chad on the on the way up, and it has a speed of 10m/s as it passes him on the way back down.Determine how fast Nicole threw the ball upwards
The speed at the 5-m level is of the same magnitude on the way up and on the way down=>
s=(v²-v₀²)/2g
Solve for v₀
-14 m/s
To determine how fast Nicole threw the ball upwards, we can use the concept of conservation of energy. When the ball is at its highest point, all of its initial kinetic energy from being thrown upwards is converted into gravitational potential energy.
At the highest point, the ball's velocity will be zero, which means its kinetic energy will also be zero. The only energy it will have is gravitational potential energy, given by the equation:
Potential Energy = mass * gravity * height,
where mass is the mass of the ball, gravity is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and height is the height above the starting point (in this case, 5 meters).
Since the mass of the ball is not given in the question, we can assume it to be 1kg for simplicity. Plugging in the values, we have:
Potential Energy = 1 kg * 9.8 m/s^2 * 5 m
= 49 Joules
Now, we can consider the ball's initial kinetic energy when it was thrown upwards. The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity^2.
Initially, the ball has some velocity (let's call it v) and we want to find that value. At its highest point, the ball's kinetic energy is converted completely into potential energy:
Kinetic Energy = Potential Energy,
0.5 * mass * v^2 = 49 Joules.
Substituting the mass as 1 kg, we can solve this equation to find the value of v:
0.5 * 1 kg * v^2 = 49 J,
0.5 * v^2 = 49 J,
v^2 = 98 J,
v = √(98 J).
Hence, the velocity with which Nicole threw the ball upwards is approximately √(98 J) or 9.899 m/s (rounded to 3 decimal places).