a ball is thrown upwards with a speed of 24 m/s.taking acceleration due to gravity as 10 m/s ,calculate the time taken when the velocity of the ball is 12 m/s when the velocity of the ball is -12 m/s what is the displacement of the ball at these time
v = 24-10t
so when is v=12 or -12?
h = 24t - 5t^2
what is h at those times?
To calculate the time taken for the velocity of the ball to be 12 m/s and -12 m/s respectively, we can use the equation of motion:
v = u + at,
where:
v = final velocity,
u = initial velocity,
a = acceleration, and
t = time.
Given that the initial velocity (u) of the ball is 24 m/s, the acceleration due to gravity (a) is 10 m/s², and the final velocities (v) are 12 m/s and -12 m/s, respectively, we can rearrange the equation:
t = (v - u) / a.
For the velocity of the ball to be 12 m/s:
t1 = (12 - 24) / -10.
t1 = -12 / -10.
t1 = 1.2 seconds.
For the velocity of the ball to be -12 m/s:
t2 = (-12 - 24) / -10.
t2 = -36 / -10.
t2 = 3.6 seconds.
Now, to calculate the displacement of the ball at these times, we can use the equation:
s = ut + (1/2)at²,
where s is the displacement.
For t1 = 1.2 seconds:
s1 = 24 * 1.2 + (1/2) * -10 * (1.2)².
s1 = 28.8 + (-7.2).
s1 = 21.6 meters.
For t2 = 3.6 seconds:
s2 = 24 * 3.6 + (1/2) * -10 * (3.6)².
s2 = 86.4 + (-64.8).
s2 = 21.6 meters.
Therefore, at both times, the displacement of the ball is 21.6 meters.
To calculate the time taken for the velocity of the ball to be 12 m/s, we can use the equation of motion:
v = u + at
Where:
v = final velocity (12 m/s)
u = initial velocity (24 m/s)
a = acceleration (-10 m/s^2, considering the acceleration due to gravity)
t = time taken
Substituting the values into the equation, we can solve for time:
12 = 24 + (-10)t
Simplifying the equation:
-10t = -12
t = (-12)/(-10)
t = 1.2 seconds
Therefore, the time taken for the velocity of the ball to be 12 m/s is 1.2 seconds.
To calculate the displacement of the ball at this time, we use another equation:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity (24 m/s)
a = acceleration (-10 m/s^2)
t = time taken (1.2 seconds)
Substituting the values into the equation:
s = (24)(1.2) + (1/2)(-10)(1.2)^2
Solving the equation:
s = 28.8 - 7.2
s = 21.6 meters
Therefore, the displacement of the ball at a time of 1.2 seconds is 21.6 meters.
To calculate the time taken for the velocity of the ball to be -12 m/s, we can use the same equation:
v = u + at
Where:
v = final velocity (-12 m/s)
u = initial velocity (24 m/s)
a = acceleration (-10 m/s^2)
t = time taken
Substituting the values into the equation, we can solve for time:
-12 = 24 + (-10)t
Simplifying the equation:
-10t = -12 - 24
t = (-36)/(-10)
t = 3.6 seconds
Therefore, the time taken for the velocity of the ball to be -12 m/s is 3.6 seconds.
To calculate the displacement of the ball at this time, we again use the equation:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity (24 m/s)
a = acceleration (-10 m/s^2)
t = time taken (3.6 seconds)
Substituting the values into the equation:
s = (24)(3.6) + (1/2)(-10)(3.6)^2
Solving the equation:
s = 86.4 - 64.8
s = 21.6 meters
Therefore, the displacement of the ball at a time of 3.6 seconds is 21.6 meters.