Question
A rock is thrown horizontally with a speed of 20 m/s from a vertical cliff of height 25 m.
How long does it take the rock to reach the horizontal ground below?
How long does it take the rock to reach the horizontal ground below?
Answers
There are no human answers yet.
Answered by
GPT 3.5
We can use the equation of motion to solve this problem. The equation is:
y = y0 + v0yt + 0.5at^2
Where:
y = final vertical displacement = 0 (since the rock reaches the ground)
y0 = initial vertical displacement = 25 m
v0y = initial vertical velocity = 0 (since the rock is thrown horizontally)
a = acceleration due to gravity = -9.8 m/s^2 (taking downward direction as negative)
t = time taken to reach the ground
Substituting the values into the equation, we get:
0 = 25 + 0 + 0.5*(-9.8)*t^2
0 = 25 - 4.9t^2
4.9t^2 = 25
t^2 = 25/4.9
t^2 = 5.102
t = sqrt(5.102)
t ≈ 2.26 seconds
Therefore, it takes approximately 2.26 seconds for the rock to reach the horizontal ground below.
y = y0 + v0yt + 0.5at^2
Where:
y = final vertical displacement = 0 (since the rock reaches the ground)
y0 = initial vertical displacement = 25 m
v0y = initial vertical velocity = 0 (since the rock is thrown horizontally)
a = acceleration due to gravity = -9.8 m/s^2 (taking downward direction as negative)
t = time taken to reach the ground
Substituting the values into the equation, we get:
0 = 25 + 0 + 0.5*(-9.8)*t^2
0 = 25 - 4.9t^2
4.9t^2 = 25
t^2 = 25/4.9
t^2 = 5.102
t = sqrt(5.102)
t ≈ 2.26 seconds
Therefore, it takes approximately 2.26 seconds for the rock to reach the horizontal ground below.
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