The acceleration due to the Earth's gravity, in English units, is 32 ft/s2. In the absence of air friction, a ball is dropped from rest. Its speed on striking the ground is exactly 60 miles/hr. For what time interval was the ball falling?
I am unsure how to set this up to solve :(
t = 2.75 s. is correct.
V = 60mi/hr * 5280Ft/mi * 1hr/3600s = 88 Ft/s.
V = Vo + g*t,
88 = 0 + 32*t,
t = ?
t=2.75
Well, if the ball's speed on striking the ground is 60 miles/hr, it seems like it was in quite a hurry! But no worries, let's figure out the time interval it was falling for.
We know that the acceleration due to gravity is 32 ft/s². Now, since we want the time in English units, we should convert the speed of the ball from miles/hr to ft/s.
By some quick calculations (and a touch of silliness), we find that 60 miles/hr is approximately 88 ft/s. So, when the ball struck the ground, its speed was 88 ft/s.
Now, we can make use of a kinematic equation:
vf = vi + at
In this case, the initial velocity (vi) is 0 ft/s, since the ball was dropped from rest. The final velocity (vf) is 88 ft/s. The acceleration (a) is -32 ft/s², as gravity acts in the opposite direction of the ball's motion.
Let's plug in the values:
88 = 0 + (-32)t
Simplifying the equation, we have:
t = -88/(-32)
Dividing those numbers, we find:
t ≈ 2.75 seconds
So, the ball was falling for approximately 2.75 seconds. Hopefully, it didn't experience a mid-air crisis!
To solve this problem, we can use the equations of motion that describe the relationship between acceleration, time, initial velocity, and final velocity. In this case, the ball is dropped from rest, so the initial velocity is 0 ft/s.
The acceleration due to gravity, g, is given as 32 ft/s². This means that the velocity of the ball is increasing by 32 ft/s every second.
We want to find the time interval for which the ball falls before hitting the ground with a speed of 60 miles/hr.
First, let's convert 60 miles/hr to ft/s:
1 mile = 5280 feet
1 hour = 3600 seconds
So, 60 miles/hr = 60 * 5280 feet / 3600 seconds ≈ 88 ft/s
We can use the equation of motion to find the time it takes for the ball to reach a speed of 88 ft/s:
v = u + at,
where:
v = final velocity (88 ft/s)
u = initial velocity (0 ft/s)
a = acceleration (-32 ft/s²) (negative because it is opposing the motion of the ball)
t = time interval (unknown)
Substituting the given values into the equation, we have:
88 ft/s = 0 ft/s + (-32 ft/s²) * t
Simplifying the equation:
88 ft/s = -32 ft/s² * t
Divide both sides of the equation by -32 ft/s²:
t = 88 ft/s / -32 ft/s²
t ≈ -2.75 s
Since time cannot be negative, we ignore the negative sign in this case.
Hence, the ball was falling for approximately 2.75 seconds.