A 5-kg ball is thrown straight up in the air with an initial speed of 24m/s. After its release and before it hits the ground when is the ball in free fall?

My answer is at all times. Is this correct? Thank you.

Correct!

1) How long does it take the ball to reach its highest point?

I am not sure what I would divide 24 by to find this.

2) How high above the starting point is the highest point?

I am not sure how to find this.

Write down the equation for the velocity as a function of time:

V(t) = V(0) - g t

where 9 = 9.81 m/s^2

Here we take the velocity positive if it is in the upward direction. When the ball is at the highest point, the velocity is zero. Clearly if the velocity is not zero, it is either going to move further upward, or if it is negative, it was at a higher point earlier.

Ok but where did the 9 come from?

I know the highest point would be 29.4 but I do not know how to get this.

There are two ways of solution

1. using kinematics.
v =vₒ - g•t,
Velocity at the highest point is zero, =>
0 = vₒ - g•t,
t =vₒ/g.
h = vₒ•t - g•t²/2 = vₒ²/2•g
2. using the law of conservation of energy
KE =PE
m•vₒ²/2 = m•g•h,
h = vₒ²/2•g.

h = (24)²/2•9.8 = 29.4 m

Yes, your answer is correct. The ball is in free fall at all times once it is released and before it hits the ground.

To understand why this is the case, let's first define what free fall means. Free fall refers to the motion of an object when it is only subject to the force of gravity and no other forces are acting on it, such as air resistance or external propulsion.

In the given scenario, when the ball is thrown straight up in the air, the only force acting on it is gravity pulling it downward. Therefore, the ball is in free fall from the moment it is released until it hits the ground.

It is important to note that during free fall, the ball will experience a changing velocity and acceleration due to the gravitational force. As the ball moves upward, gravity slows down its velocity until it reaches its maximum height. Then, gravity accelerates the ball downward, causing it to gain speed until it eventually hits the ground. So, during its entire motion, the ball is indeed in free fall.