if a rock is dropped from the top of a 200 ft building, solve for the time it takes for it to hit the ground. (when h=0)
hint-initial velocity when dropped is 0
in non-metric units
h = -16t^2 + 0t + 200 , where t is in seconds and h is in feet
so when it hits the ground , h = 0
so 0 = -16t^2 + 200
16t^2 = 200
t = √(200/16) = 10√2/4
= 5√2/2 or appr 3.54 seconds
To solve for the time it takes for the rock to hit the ground, we can use the kinematic equation that relates the distance traveled by an object in free fall to time:
h = (1/2)gt^2
where:
h is the height (set to 200 ft initially and 0 ft when it hits the ground)
g is the acceleration due to gravity (approximately 32 ft/s^2)
t is the time it takes for the rock to hit the ground.
Since the initial velocity of the rock is 0 when it is dropped, we can set h = 200 ft and solve for t:
200 = (1/2)(32)(t^2)
To solve for t, let's rearrange the equation:
t^2 = 2 * (200/32)
t^2 = 12.5
Now, take the square root of both sides to find the value of t:
t ≈ sqrt(12.5)
t ≈ 3.54 seconds.
Therefore, it takes approximately 3.54 seconds for the rock to hit the ground when dropped from a 200 ft building.
To solve for the time it takes for the rock to hit the ground when dropped from a 200 ft building, we can use the equation of motion:
h(t) = 0.5*g*t^2 + v0*t + h0
Where:
h(t) is the height of the object at time t
g is the acceleration due to gravity (approximately 32.2 ft/s^2)
t is the time in seconds
v0 is the initial velocity (0 ft/s in this case)
h0 is the initial height (200 ft)
In this case, we want to find the time when h(t) is equal to 0.
Plugging in the given values, the equation becomes:
0 = 0.5*32.2*t^2 + 0*t + 200
Simplifying the equation, we get:
0 = 16.1*t^2 + 200
To solve for t, we need to isolate t^2. Subtracting 200 from both sides of the equation:
-200 = 16.1*t^2
Dividing both sides by 16.1:
t^2 = -200/16.1
Taking the square root of both sides:
t = ±√(-200/16.1)
As time cannot be negative in this context, we can disregard the negative square root. So, the time it takes for the rock to hit the ground is:
t = √(-200/16.1)
Calculating this using a calculator, we find:
t ≈ 2.52 seconds
Therefore, it takes approximately 2.52 seconds for the rock to hit the ground when dropped from a 200 ft building.