a ball is shot upwards from ground level at a vertical speed of 40 m/s.

a. What is the vertical speed of the ball just as it hits the ground? Explain.

b. How long is the ball in the air? Explain.

c. Draw a height vs time graph of the situation. Include a point at each 1-second interval

a. 40 m/s down

potential energy = m g h
same h
so same potential energy
so same kinetic energy (1/2)m v^2

b.
how long up
0 = 40 - g t
t = 40/9.81
2 t = time up + time down = 80/9.81

a parabola, sheds water
y = 40 t - 4.9 t^2

a. To determine the vertical speed of the ball just as it hits the ground, we need to consider the concept of freefall and use the equations of motion. In freefall, the only force acting on an object is gravity. Initially, the ball is shot upwards with a vertical speed of 40 m/s. As the ball reaches its peak height, its vertical speed decreases due to the acceleration of gravity acting in the opposite direction. When the ball reaches its highest point, its vertical speed becomes zero. On its way back down, the ball accelerates due to gravity, increasing its vertical speed. When the ball hits the ground, its vertical speed will be the same as it was just before it was shot up initially. Therefore, the vertical speed of the ball just as it hits the ground will also be 40 m/s.

b. To calculate the total time the ball is in the air, we can use the equation of motion:

time = (final velocity - initial velocity) / acceleration

At the highest point, the final velocity is 0 m/s, and the initial velocity is 40 m/s (upward velocity). The acceleration is the acceleration due to gravity, which is approximately -9.8 m/s² (assuming upward direction as positive).

Plugging these values into the equation, we get:

time = (0 - 40) / -9.8
= 4.08 seconds (rounded to two decimal places)

Therefore, the ball is in the air for approximately 4.08 seconds.

c. The height vs. time graph of the situation can be represented as follows:

Time (s) | Height (m)
-------------------
0 | 0
1 | 40
2 | 60
3 | 60
4 | 40
5 | 0

In this graph, the height increases as the ball is shot up, reaches its peak height at 2 seconds, and then falls back down to the ground. The height vs. time graph has a bell-shaped curve, reflecting the ball's upward and downward motion.