An object projected horizontally from the top of a cliff with a velocity of 7 metre per second and land on the ground level a point 56m from the base of the cliff calculate the height of the cliff
The formula is h=ut+1/2gtsqare,so we are gonna fix the parameters
h=0×8+1/2×10×8sqare
h=0+1/2×10×64
h=5×64
h=320m
56m / 7m/s = 8s
so, how far does it fall in 8 seconds?
H=320m
Oh, "height of the cliff," that's a tall ask! But don't worry, I'm here to help.
To calculate the height of the cliff, we can use the equations of motion. Since the object is projected horizontally, its initial vertical velocity is zero. The equation we need is:
h = (1/2) * g * t^2
Where:
h = height of the cliff
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken to hit the ground (which is the same as the time taken to cover 56m horizontally)
To find the time, we can use:
56m = 7m/s * t
Solving for t, we get:
t = 56m / 7m/s
Now we can substitute this value of t back into the equation for h:
h = (1/2) * 9.8m/s^2 * (56m / 7m/s)^2
By simplifying and calculating, we find:
h ≈ 158.4 meters
So, the height of the cliff is approximately 158.4 meters. Now that's a cliff worth talking about!
To calculate the height of the cliff, we can use the equation of motion for horizontal projectile motion:
Range = Horizontal velocity * Time
In this case, the horizontal velocity is given as 7 m/s and the range (distance traveled horizontally) is given as 56 meters. So, we can rearrange the equation to solve for time.
Time = Range / Horizontal velocity
Time = 56 m / 7 m/s = 8 seconds
Now, to find the height of the cliff, we can use the equation of motion for vertical projectile motion:
Height = (Vertical velocity * Time) - (0.5 * Gravity * Time^2)
Since the object is projected horizontally, the vertical velocity is initially zero. The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values, we get:
Height = 0 - (0.5 * 9.8 m/s^2 * (8 s)^2)
Height = -39.2 m
The negative sign indicates that the object is below the reference point, which is the ground level. Therefore, the height of the cliff is 39.2 meters.