Answer :
Final answer:
To solve this problem, we first need to calculate the time when the boulder is moving at a speed of 19.4 m/s upward and downward. The displacement of the boulder from its initial position is zero when it is at the highest point of its trajectory. The velocity of the boulder is zero at the highest point of its trajectory and at the end of its motion.
Explanation:
To solve this problem, we first need to calculate the time (a) when the boulder is moving at a speed of 19.4 m/s upward and (b) when it is moving at a speed of 19.4 m/s downward. We can use the equations of motion to find these times. The time when the boulder is moving at a speed of 19.4 m/s upward is approximately 1.44 seconds and the time when it is moving at a speed of 19.4 m/s downward is approximately 3.76 seconds.
(c) The displacement of the boulder from its initial position would be zero when it is at the highest point of its trajectory, which occurs halfway through its total time of flight. So, the displacement is zero at approximately 2.50 seconds.
(d) The velocity of the boulder is zero at the highest point of its trajectory and at the end of its motion. Therefore, the velocity is zero at approximately 2.50 seconds and 5.00 seconds.
(e) The magnitude of the acceleration while the boulder is moving can be calculated using the equation a = Δv/t, where Δv is the change in velocity and t is the time interval. Since the boulder is thrown vertically upward, the acceleration due to gravity is the only acceleration acting on it. Therefore, the magnitude of the acceleration is approximately 9.8 m/s².
(f) The direction of the acceleration while the boulder is moving is always downward, towards the center of the Earth, regardless of the direction of its motion. This is because the acceleration due to gravity always acts in the opposite direction to the motion of the object.
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