To find the velocity of the stone just before reaching the ground, we need to consider the motion of the stone in two parts: its upward motion and its downward motion.
- Upward motion: The initial velocity of the stone is 20 m/s, and it is thrown upward against the force of gravity. The acceleration due to gravity (g) is -10 m/s² (negative because it acts in the opposite direction to the motion). Using the equation of motion:
v = u + gt
where: v = final velocity u = initial velocity g = acceleration due to gravity t = time
Plugging in the values:
v_up = 20 - 10t
- Downward motion: When the stone reaches its highest point, its velocity will become zero. From that point onward, the stone will start falling downward under the influence of gravity. We can find the time it takes to reach the highest point using the equation:
v = u + gt
At the highest point, the final velocity (v) is zero. The initial velocity (u) is 20 m/s, and the acceleration due to gravity (g) is -10 m/s².
0 = 20 - 10t_highest
Solving for t_highest:
10t_highest = 20 t_highest = 2 seconds
Now, we can find the total time of flight (t_total) by doubling the time to reach the highest point:
t_total = 2 * t_highest t_total = 2 * 2 t_total = 4 seconds
Finally, we can find the velocity just before reaching the ground by substituting the total time of flight (t_total) into the equation for the upward motion:
v_down = v_up = 20 - 10t_total v_down = 20 - 10 * 4 v_down = 20 - 40 v_down = -20 m/s
Therefore, the velocity of the stone just before reaching the ground is -20 m/s. The negative sign indicates that the velocity is in the downward direction.