Question 1)
A rock is dropped from the top of a 100 meter tall cliff.
A. ) How long will it take for the rock to reach the ground.
B) What will be the velocity of the rock when it hits the ground?
C) How long will it take for the rock to reach the ground if the rock is thrown upward initially at 12 m/s?
h = -4.9t^2 + 100
A.
to reach the ground h = 0
0 = -4.9t^2 + 100
4.9t^2 = 100
t^2 = 100/4.9
t = √(100/4.9) = appr 4.5 seconds
B.
v = -9.8t
sub in t = 4.5
C.
original equation is
h = -4.9t^2 + 12t + 100
set equal to zero again, and solve using the quadratic equation. Take the positive result and ignore the negative answer.
To answer these questions, we can use the equations of motion in physics. Let's go step by step.
A) How long will it take for the rock to reach the ground?
The time it takes for an object to fall from a height h can be calculated using the equation:
t = √(2h/g),
where t is the time, h is the height, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the height of the cliff is 100 meters. Plugging these values into the equation, we get:
t = √(2 * 100 / 9.8) ≈ 4.04 seconds.
So, it will take approximately 4.04 seconds for the rock to reach the ground.
B) What will be the velocity of the rock when it hits the ground?
The final velocity of an object falling from a height without any initial velocity can be calculated using the equation:
v = √(2gh),
where v is the final velocity and h is the height.
Plugging in the values, we get:
v = √(2 * 9.8 * 100) ≈ 44.3 m/s.
Therefore, the velocity of the rock when it hits the ground is approximately 44.3 m/s.
C) How long will it take for the rock to reach the ground if the rock is thrown upward initially at 12 m/s?
In this case, the initial velocity is 12 m/s. We can use the equation of motion:
t = (v - u) / g,
where t is the time, v is the final velocity, u is the initial velocity, and g is the acceleration due to gravity.
Since the rock is thrown upward, the final velocity is 0 m/s, and the initial velocity is 12 m/s. Plugging in the values, we get:
t = (0 - 12) / (-9.8) ≈ 1.22 seconds.
Therefore, it will take approximately 1.22 seconds for the rock to reach the ground if it is thrown upward initially at 12 m/s.