Part 1:
A ball is thrown horizontally from the top of a building 28.6 m high. The ball strikes the ground at a point 80.3 m from the base of the building.
The acceleration of gravity is 9.8 m/s^2. Find the time the ball is in motion. Answer in units of s.
Part 2:
Find the initial velocity of the ball. Answer in units of m/s.
Part 3:
Find the x componet of its velocity just before it strikes the ground. Answer in units of m/s.
Part 4:
Find the y componet of its velocity just before it strikes the ground. Answer in units of m/s.
No one has answered this question yet.
Part 1: To find the time the ball is in motion, we can use the equation of motion for an object in free fall:
h = (1/2)gt^2
where h is the height, g is the acceleration due to gravity, and t is the time. In this case, the height is 28.6 m and the vertical component of the ball's motion is in free fall, so the equation becomes:
28.6 = (1/2)(9.8)t^2
Now, solve for t:
28.6 = 4.9t^2
Divide both sides by 4.9:
t^2 = 5.83673469
Take the square root of both sides to find t:
t = √(5.83673469)
t ≈ 2.42 seconds
So, the ball is in motion for approximately 2.42 seconds.
Part 2: To find the initial velocity of the ball, we can use the equation of motion for an object in free fall:
v = gt
where v is the initial velocity, g is the acceleration due to gravity, and t is the time. The horizontal component of the ball's motion remains constant, so the velocity in the x-direction is the same as the initial velocity. In this case, g is 9.8 m/s^2 and t is 2.42 seconds:
v = (9.8)(2.42)
v ≈ 23.716 m/s
So, the initial velocity of the ball is approximately 23.716 m/s.
Part 3: The x-component of the ball's velocity just before it strikes the ground can be found using the equation of motion for constant velocity:
v = (d/t)
where v is the velocity, d is the displacement, and t is the time. In this case, the displacement is 80.3 m and the time is 2.42 seconds. Since the ball is moving horizontally, the x-component of its velocity remains constant:
v_x = (80.3/2.42)
v_x ≈ 33.18 m/s
So, the x-component of the ball's velocity just before it strikes the ground is approximately 33.18 m/s.
Part 4: The y-component of the ball's velocity just before it strikes the ground can be found using the equation of motion for an object in free fall:
v = gt
where v is the velocity, g is the acceleration due to gravity, and t is the time. In this case, g is 9.8 m/s^2 and t is 2.42 seconds:
v_y = (9.8)(2.42)
v_y ≈ 23.716 m/s
So, the y-component of the ball's velocity just before it strikes the ground is approximately 23.716 m/s.