A rock is thrown vertically upward with an initial speed of 100 ft/s. At the same instant another rock is thrown vertically downward from the top of a 280 ft cliff with an initial speed of 40 ft/s. Neglecting air friction,
Yes
A rock is thrown vertically upward with an initial speed of 100 ft/s. At the same instant another rock is thrown vertically downward from the top of a 280 ft cliff with an initial speed of 40 ft/s.
To find the time it takes for the first rock to reach its highest point, we can use the formula:
v = u + at
Where:
v = final velocity (0 ft/s when it reaches its highest point)
u = initial velocity (100 ft/s)
a = acceleration (gravitational acceleration, -32 ft/s² considering upward direction as positive)
t = time
Rearranging the equation to solve for time, we have:
0 = 100 - 32t
Simplifying further:
32t = 100
t = 100 / 32
t ≈ 3.13 seconds
Now, to find the time it takes for the second rock to fall from the top of the cliff, we can use the same formula with the initial velocity as -40 ft/s (considering downward direction as negative).
Rearranging the equation:
0 = -40 + 32t
Simplifying further:
32t = 40
t = 40 / 32
t ≈ 1.25 seconds
Therefore, the time it takes for the first rock to reach its highest point is approximately 3.13 seconds, and the time it takes for the second rock to fall from the top of the cliff is approximately 1.25 seconds.