Free fall equation is s=6.1t^2 ft, where t is in seconds. Assume a rock is dropped from a 100 ft cliff. Find speed of the rock at t=3.5 sec.
v = ds/dt = 32.2t
how is 2*6.1 equal to 32.2??
To find the speed of the rock at t = 3.5 seconds, we need to use the equation for free fall motion:
s = 6.1t^2
Where:
s - is the distance fallen in feet
t - is the time in seconds
First, we need to calculate the distance fallen by the rock at t = 3.5 seconds.
Substituting t = 3.5 into the equation:
s = 6.1(3.5^2)
s = 72.575 ft
So, at t = 3.5 seconds, the rock has fallen 72.575 ft.
To find the speed of the rock at t = 3.5 seconds, we can use the formula:
Speed (v) = Distance (s) / Time (t)
The distance is the distance fallen, which is 72.575 ft, and the time is 3.5 seconds.
Plugging in the values:
v = 72.575 ft / 3.5 sec
v ≈ 20.73 ft/s
Therefore, the speed of the rock at t = 3.5 seconds is approximately 20.73 ft/s.