SAMPLE PROBLEM:
A ball is thrown horizontally from a height of 6m with an initial speed of 20m/s. (a.)How long will it take the ball to reach the ground? (b)At what horizontal distance from the point of release will it strike the ground? (c) What will be the magnitude of its velocity when it strikes the ground? (d) At what angle will it strike the ground?
Answers & Comments
To solve the given sample problem, we can use the equations of motion for projectile motion. Since the ball is thrown horizontally, its initial vertical velocity is 0 m/s.
(a) To find the time it takes for the ball to reach the ground, we can use the equation:
h = (1/2) * g * t^2
Where:
h = height of the ball = 6 m
g = acceleration due to gravity = 9.8 m/s^2
t = time
Rearranging the equation to solve for time:
t = sqrt((2 * h) / g)
t = sqrt((2 * 6) / 9.8)
t ≈ 1.23 seconds
Therefore, it will take approximately 1.23 seconds for the ball to reach the ground.
(b) To find the horizontal distance from the point of release where the ball will strike the ground, we can use the equation:
d = v * t
Where:
d = horizontal distance
v = horizontal velocity
t = time
Since the ball is thrown horizontally, the horizontal velocity remains constant throughout its motion. Thus, the horizontal velocity is 20 m/s.
d = 20 * 1.23
d ≈ 24.6 meters
Therefore, the ball will strike the ground at a horizontal distance of approximately 24.6 meters from the point of release.
(c) Since the ball is thrown horizontally, its initial vertical velocity is 0 m/s. As it falls, it gains vertical velocity due to the acceleration due to gravity. The magnitude of its final velocity when it strikes the ground can be found using the equation:
v_final = g * t
v_final = 9.8 * 1.23
v_final ≈ 12.05 m/s
Therefore, the magnitude of the ball's velocity when it strikes the ground is approximately 12.05 m/s.
(d) Since the ball is thrown horizontally, it will strike the ground at an angle of 0 degrees or horizontally.
To summarize:
(a) It will take approximately 1.23 seconds for the ball to reach the ground.
(b) The ball will strike the ground at a horizontal distance of approximately 24.6 meters from the point of release.
(c) The magnitude of the ball's velocity when it strikes the ground is approximately 12.05 m/s.
(d) The ball will strike the ground at an angle of 0 degrees or horizontally.