Bull A is dropped form a balcony 19,6 m from the ground. At the same time an identical B is projected vertical downwards from the top of a building a 29, 6 m from the ground.
Calculating magnitude of the :
3.1 final velocity of the ball A
3.2 velocity with which B must be projected to reach the ground at a same time as A
To solve this problem, we can use the equations of motion and the principles of physics.
3.1 Calculating the final velocity of ball A:
We can start by calculating the time it takes for ball A to fall from the balcony to the ground. We can use the equation:
h = (1/2)gt^2,
where h is the height (19.6 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Rearranging the equation, we can solve for t:
t^2 = (2h) / g,
t^2 = (2 * 19.6) / 9.8,
t^2 = 39.2 / 9.8,
t^2 = 4,
t = 2 seconds.
Now that we know the time, we can calculate the final velocity of ball A using the equation:
v = gt,
where v is the final velocity, g is the acceleration due to gravity, and t is the time.
v = (9.8 m/s^2) * (2 s),
v = 19.6 m/s.
Therefore, the final velocity of ball A is 19.6 m/s.
3.2 Calculating the velocity with which B must be projected to reach the ground at the same time as A:
To reach the ground at the same time as ball A, ball B must travel a vertical distance of 29.6 m. We can use the equation:
h = (1/2)gt^2,
where h is the height (29.6 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Rearranging the equation, we can solve for t:
t^2 = (2h) / g,
t^2 = (2 * 29.6) / 9.8,
t^2 = 59.2 / 9.8,
t^2 = 6,
t = √6 seconds.
Now, to calculate the initial velocity needed for ball B to reach the ground at the same time as A, we can use the equation:
h = ut + (1/2)gt^2,
where h is the height (29.6 m), u is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Plugging in the known values, we have:
29.6 = u*(√6) + (1/2)*(9.8)*(√6)^2,
29.6 = u*(√6) + (1/2)*(9.8)*(6),
29.6 = u*(√6) + (29.4),
29.6 - 29.4 = u*(√6),
0.2 = u*(√6),
u = 0.2 / (√6),
u ≈ 0.082 m/s.
Therefore, the velocity with which B must be projected to reach the ground at the same time as A is approximately 0.082 m/s.