a. d = Vo*t = 60 m
26 * t = 60
t = 2.31 s. = Fall time.
h = 0.5g*t^2 = 4.9*2.31^2 = 26.1 m.
b. h = Same as part a.
Which I got this answer below.
h= 26.1 m
How do I solve for the one below.
If it takes a ball dropped from rest 2.308s to fall to the ground, from what height H was it released?
26 * t = 60
t = 2.31 s. = Fall time.
h = 0.5g*t^2 = 4.9*2.31^2 = 26.1 m.
b. h = Same as part a.
We know that the time it takes for the ball to fall is 2.308 seconds. Now, we can use a little bit of physics magic called gravity to help us out. Gravity is a downward force that causes objects to accelerate towards the ground. In this case, we're dealing with a ball being dropped, so it's accelerating at a rate of 9.8 m/s² (approximately, for all you sticklers out there).
Now, we can use a lovely little equation: h = (1/2)gt². In this equation, h represents the height, g represents the acceleration due to gravity, and t represents the time it takes for the ball to fall. Plugging in the numbers we have, we get:
h = (1/2)(9.8 m/s²)(2.308 s)²
Calculating this little equation, we find that h ≈ 25.9 m.
And there you have it! The ball was released from a height of approximately 25.9 meters. Keep in mind that this is an approximation due to the approximate value of g. But hey, it's close enough for all the non-scientific purposes, right? Happy falling!
H = 0.5 * g * t^2
where H is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time it takes for the object to fall.
In this case, the time taken is 2.308 seconds. So, substituting the values into the equation:
H = 0.5 * 9.8 m/s^2 * (2.308 s)^2
H = 0.5 * 9.8 m/s^2 * 5.316864 s^2
H = 25.962416 m
Therefore, the ball was released from a height of approximately 25.96 meters (or rounding to two decimal places, 26.0 meters).
h = vi * t + (1/2) * g * t^2
where:
h is the height
vi is the initial velocity (0 m/s for a ball dropped from rest)
t is the time of fall
g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, we are given the time of fall, t = 2.308 s. We can substitute this value into the equation and solve for h.
h = 0 * 2.308 + (1/2) * 9.8 * (2.308)^2
Simplifying the equation gives:
h = (1/2) * 9.8 * 5.312064
h ≈ 25.989 m
Therefore, the ball was released from a height of approximately 25.989 meters.