A particle is projected at 10ms^-1 from a height of 45m. Calculate the horizontal distance covered by the particle before reaching the ground(g=10ms^-2)
assuming it was projected horizontally, then since distance=speed*time, all you need to do is figure out how long it takes to fall 45m:
4.9t^2 = 45
45=(1/2 )10t*2 solve for t=2 seconds .d=10t=10*2=20m
To calculate the horizontal distance covered by the particle before reaching the ground, we can use the kinematic equation:
d = v * t
Where:
d = horizontal distance
v = horizontal velocity
t = time
We need to find the time it takes for the particle to reach the ground. Since the particle is projected vertically, we can use the equation for vertical displacement:
s = ut + (1/2)gt^2
Where:
s = vertical displacement (height)
u = initial vertical velocity
g = acceleration due to gravity
t = time
We know the initial vertical velocity (u) is 10 m/s, the height (s) is 45 m, and the acceleration due to gravity (g) is 10 m/s^2. Solving for t:
45 = 10t + (1/2)(10)(t^2)
45 = 10t + 5t^2
5t^2 + 10t - 45 = 0
We can solve this quadratic equation to find the value of t. Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 5, b = 10, and c = -45. Substituting these values into the quadratic formula:
t = (-10 ± √(10^2 - 4 * 5 * -45)) / (2 * 5)
t = (-10 ± √(100 + 900)) / 10
t = (-10 ± √1000) / 10
t = (-10 ± 31.62) / 10
Using the positive value, t = (31.62 - 10) / 10 = 21.62 / 10 = 2.162 seconds.
Now that we have the time, we can calculate the horizontal distance (d):
d = v * t
d = 10 m/s * 2.162 s
d = 21.62 meters
Therefore, the horizontal distance covered by the particle before reaching the ground is 21.62 meters.
To calculate the horizontal distance covered by the particle, we will need to find the time it takes for the particle to reach the ground.
First, we need to determine the time taken for the particle to fall from a height of 45m. We can use the equation of motion:
h = (1/2) * g * t^2
where:
h = height
g = acceleration due to gravity
t = time
Rearranging the equation, we get:
t = sqrt(2h / g)
Plugging in the values, we have:
t = sqrt(2 * 45 / 10)
t ≈ 3 seconds
Now that we know the time it takes for the particle to fall, we can calculate the horizontal distance covered. The formula to calculate the distance d is:
d = v * t
where:
v = initial velocity in the horizontal direction
t = time
In this case, the initial velocity in the horizontal direction is given as 10 m/s, and the time taken is 3 seconds. So, plugging in the values:
d = 10 * 3
d = 30 meters
Therefore, the horizontal distance covered by the particle before reaching the ground is 30 meters.