From the top of a cliff 80m heigh a stone is projected horizontally with a speed of 20m/s how far from the stone strike the ground?
falling 80 m:
80= 4.9 t^2
solve for fall time t
then horizontal problem:
d = 20 t
I really don't know the answer and also not familiar to physics
To find how far from the stone will strike the ground, we can calculate the horizontal distance the stone travels in the time it takes to reach the ground.
First, let's find the time it takes for the stone to reach the ground using the given information. We know that the initial vertical velocity of the stone is 0 m/s since it is projected horizontally. The acceleration due to gravity is approximately -9.8 m/s² (negative because it acts downwards). The initial vertical position is 80 m.
We can use the following formula to find the time it takes for an object to fall freely:
s = ut + (1/2)gt²
where:
s = vertical displacement (final position - initial position)
u = initial vertical velocity
t = time
g = acceleration due to gravity
Rearranging the formula, we have:
t = sqrt(2s/g)
Substituting the known values:
t = sqrt(2 * 80 / 9.8)
t = sqrt(160 / 9.8)
t ≈ sqrt(16.33)
t ≈ 4.04 seconds (rounded to two decimal places)
Now, let's find the horizontal distance traveled by the stone during this time. Since the stone is projected horizontally with a speed of 20 m/s, the horizontal distance is given by:
Distance = speed * time
Distance = 20 m/s * 4.04 s
Distance ≈ 80.8 meters
Therefore, the stone will strike the ground approximately 80.8 meters horizontally from the point it was projected.
To determine how far from the stone strike the ground, we can use the principles of projectile motion. In this case, the stone is projected horizontally, so it will only be influenced by gravity in the vertical direction.
First, let's analyze the motion in the vertical direction. We can use the following equation to calculate the time it takes for the stone to reach the ground:
h = (1/2) * g * t^2
Where:
h is the initial height (80m)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time it takes for the stone to reach the ground (which we want to find)
Rearranging the equation, we have:
t = sqrt(2h / g)
Plugging in the values:
t = sqrt(2 * 80 / 9.8)
t ≈ 4.04 seconds
Now that we've found the time it takes for the stone to reach the ground, let's calculate the horizontal distance it travels. Since it is projected horizontally, its horizontal velocity (Vx) remains constant throughout the motion, which is given as 20 m/s.
Using the equation:
d = Vx * t
where:
d is the horizontal distance
Vx is the horizontal velocity (20 m/s)
t is the time (4.04 seconds)
Plugging in the values:
d = 20 * 4.04
d ≈ 80.8 meters
Therefore, the stone will strike the ground approximately 80.8 meters away horizontally.